Category Archives: Music

Recommendations, thoughts and memories…

Circle Theorems

This article explains circle theorems, including tangents, sectors, angles and proofs (with thanks to Revision Maths).

Isosceles Triangle

Two Radii and a chord make an isosceles triangle.

Perpendicular Chord Bisection

The perpendicular from the centre of a circle to a chord will always bisect the chord (split it into two equal lengths).

Angles Subtended on the Same Arc

Angles subtended on the same arc

Angles formed from two points on the circumference are equal to other angles, in the same arc, formed from those two points.

Angle in a Semi-Circle

angle in a semi-circle

Angles formed by drawing lines from the ends of the diameter of a circle to its circumference form a right angle. So c is a right angle.


We can split the triangle in two by drawing a line from the centre of the circle to the point on the circumference our triangle touches.

Divide the triangle in two

We know that each of the lines which is a radius of the circle (the green lines) are the same length. Therefore each of the two triangles is isosceles and has a pair of equal angles.

Two isosceles triangles

But all of these angles together must add up to 180°, since they are the angles of the original big triangle.

Therefore x + y + x + y = 180, in other words 2(x + y) = 180.
and so x + y = 90. But x + y is the size of the angle we wanted to find.


A tangent to a circle is a straight line which touches the circle at only one point (so it does not cross the circle- it just touches it).

A tangent to a circle forms a right angle with the circle’s radius, at the point of contact of the tangent.

angle with a tangent

Also, if two tangents are drawn on a circle and they cross, the lengths of the two tangents (from the point where they touch the circle to the point where they cross) will be the same.

Tangents from an external point are equal in length

Angle at the Centre

Angle at the centre

The angle formed at the centre of the circle by lines originating from two points on the circle’s circumference is double the angle formed on the circumference of the circle by lines originating from the same points. i.e. a = 2b.


You might have to be able to prove this fact:

proof diagram 1

OA = OX since both of these are equal to the radius of the circle. The triangle AOX is therefore isosceles and so ∠OXA = a
Similarly, ∠OXB = b

proof diagram 2

Since the angles in a triangle add up to 180, we know that ∠XOA = 180 – 2a
Similarly, ∠BOX = 180 – 2b
Since the angles around a point add up to 360, we have that ∠AOB = 360 – ∠XOA – ∠BOX
= 360 – (180 – 2a) – (180 – 2b)
= 2a + 2b = 2(a + b) = 2 ∠AXB

Alternate Segment Theorem

Alternate segment theorem

This diagram shows the alternate segment theorem. In short, the red angles are equal to each other and the green angles are equal to each other.


You may have to be able to prove the alternate segment theorem:

proof of alternate segment theorem

We use facts about related angles

A tangent makes an angle of 90 degrees with the radius of a circle, so we know that ∠OAC + x = 90.
The angle in a semi-circle is 90, so ∠BCA = 90.
The angles in a triangle add up to 180, so ∠BCA + ∠OAC + y = 180
Therefore 90 + ∠OAC + y = 180 and so ∠OAC + y = 90
But OAC + x = 90, so ∠OAC + x = ∠OAC + y
Hence x = y

Cyclic Quadrilaterals

cyclic quadrilateral is a four-sided figure in a circle, with each vertex (corner) of the quadrilateral touching the circumference of the circle. The opposite angles of such a quadrilateral add up to 180 degrees.

Area of Sector and Arc Length

A sector

If the radius of the circle is r,
Area of sector = πr2 × A/360
Arc length = 2πr × A/360

In other words, area of sector = area of circle × A/360
arc length = circumference of circle × A/360

Musical Memories

Whether it’s the food I eat, the drinks I enjoy or the music I listen to, the main reason always seems to be a particular memory of a place, a person or a moment. This is a list of my favourite music with a few autobiographical grace notes…

ABBATake A Chance On Me My sister bought the single and I still remember I’m A Marionette on the B-side!
Amy StroupAlas We Aspire
Anna NalickBreathe (2 A.M.)
Annie LennoxWaiting In VainCall me a softie, but Kate Beckinsale in Serendipity
Annie LennoxWalking On Broken GlassMy dancing partner Vicki Kereszteny found this for rehearsing our cha
Apollo 440Stop The RockClaire Forlani at the foam party in Boys and Girls
BeatlesHere Comes The SunDoes anyone remember this as the theme to the Holiday programme…?!
BeatlesLet It BeI sang this to myself while cycling to every one of my finals
Bell X1Eve, the Apple of My Eye
BerlinTake My Breath AwayWho can forget the Top Gun theme…?!
Bette MidlerIn My Life
Bette MidlerFrom A Distance
Billy JoelMy LifeThis was the theme to Bosom Buddies, which gave us Tom Hanks and Donna Dixon!
Black Eyed PeasI Gotta Feeling
BlurTo The EndWatching Blur at Mile End in the rain
Bon JoviLivin’ On A PrayerWatching with Joe Oatley in Milton Keynes as he walked in front of 12′ screens full of feedback snow!
Boyz II MenEnd Of The RoadVicki gave me the Brit Awards CD from 1993, and this was on it…
Bruce SpringsteenBorn In The USAOne of the best presents I ever had was the MTV Plugged CD given me by Mark Highman, and all these songs were on it…
Bruce SpringsteenI Wish I Were Blind
Bruce SpringsteenThunder Road (MTV Plugged)
Bruce SpringsteenMy Beautiful Reward
Bryan FerryOh Yeah (On The Radio)
Bryan FerryMore Than This
CarsYou Might ThinkMy first girlfriend Paula Buster from Canyon, TX
Carter BurwellOvertureI have a soft spot for great theme tunes, and Carter Burwell pulled out all the stops for Conspiracy Theory
Carter BurwellConspiracy Theory
Carter BurwellRiding
ChicaneDon’t Give Up
ChicaneNo Ordinary MorningTo Anne Crary, the only girl I ever asked to marry me, who introduced me to Chicane when I tried to put on the Bee Gees!
Clem SnideMoment In The Sun
Corey HartSunglasses At NightAnother one from my time in the States with Paula
Craig AmstrongPortuguese Love ThemeLove, Actually didn’t go down well with the Belgians next to me, but to me it was as if the director had exactly the same view of love (and good music!)
Craig AmstrongGlasgow Love Theme
Craig AmstrongPM’s Love Theme
David BowieRebel Rebel
David BowieLife On Mars?
David GatesGoodbye GirlThe Goodbye Girl is one of the great (forgotten) romantic comedies. Richard Dreyfus and Marsha Mason at their best.
David GrayDisappearing WorldTo my musical friend Eden James, who introduced me to David Gray in Brisbane when we ended up singing along to the guitar (and the odd possum on the roof!) after every house party…
David GrayBabylon
David GrayMy Oh My
David GrayPlease Forgive Me
David Gray
David Gray
David GrayJanuary Rain
David GrayThe Other Side
DidoHere With MeI have a bit of a weakness for US teen dramas, so I was easy meat for Shiri Appleby in Roswell
Dire StraitsRomeo And JulietWhen I made the mistake of showing my diary to Elizabeth at Oxford, this is what I taped back-to-back and listened to over and over again to make the break-up hurt a bit less
Dire StraitsSo Far Away
Dire StraitsSultans Of Swing (Live Aid)When I was away in Germany, I had to ask my mum to tape Live Aid, but this was the only song I liked (until I accidentally pressed the record button on my tape deck and had to do without it until Napster came along!)
Dire StraitsYour Latest Trick
Dire StraitsTelegraph Road
Dire StraitsPrivate Investigations
Don HenleyThe Boys Of Summer
Emily Barker & The Red Clay HaloPauseAnother great TV theme from The Shadow Line
Etta JamesAt Last
Fats Waller & Benny PayneAfter You’ve GoneThe other contender for the greatest present of all time. I told Claudine Kenny this was my favourite (unobtainable) jazz track, and she managed to track it down for my birthday.
Fine Young CannibalsGood Thing
Flo RidaClub Can’t Handle Me
Foo FightersNext Year
Frank SinatraOne For My BabyOne of the few songs to which I know all the words, which was embarrassing when my mum caught me singing it in Newton Abbot!
Geoffrey BurgonBrideshead RevisitedOne of the happiest moments of my life came when we all trudged across the gravel on a perfect sunny October morning at Christ Church to have our matriculation photograph taken…and the second years played this from one of the windows in Peck! (They were fined £150…)
Gerry RaffertyBaker StreetMy sister caught sight of a list I was making of my favourite music and made me a couple of treasured mix tapes including this classic of urban disaffection
HaddawayWhat Is LoveAnother one from the Brit Awards CD from Vicki
Herbie HancockCantaloupe IslandMy friend Tio made me a tape of ‘E-type jazz’ in exchange for a ride down the King’s Road in my 1965 carmine red Series 2 roadster, and this was my favourite
Herbie HancockDriftin’
Imogen HeapHide And SeekI heard this played over the funeral scene in The OC, so it was perhaps inevitable I should end up living there (Ormonde Court, not Orange County!)
Jon & VangelisI’ll Find My Way Home
KasabianClub FootI actually met Kasabian while playing the referee in Sky Sports’ last World Cup advert!
Kate BushWuthering HeightsThanks again to my sister Katharine for buying The Kick Inside. Did Kate Bush really write these songs when she was only 19?! Astonishing…
Little FeatWillin’One of the best days of my life came when I took a day off to visit Singapore for a birthday treat for my ex-boss at Mercer. Champagne breakfast, waterskiing, sevens, a rickshaw ride, Singapore slings in Raffles, two beautiful girls and this song…
Loreena McKennittDante’s PrayerMore thanks to Anne Crary for introducing me to this
Lynyrd SkynyrdTuesday’s Gone
Marshall CrenshawSomeday, Someway
Martin Solveig & DragonetteHello (Single Edit)
Matt CardleWhen We Collide
Miley CyrusWhen I Look At You
Morten LauridsenO Magnum MysteriumI heard this for the first time sitting next to Marina at a concert given by our friend Sam’s choir, and we were both blown away. What a perfect way to discover a wonderful piece!
MussorgskyThe Great Gate of Kiev
Nick LoweI Love The Sound Of Breaking GlassThis memory is so far back, I don’t even know where it came from, but 1978 was a great year for new music (think Wuthering Heights!)
Norah JonesTurn Me On
Norah JonesThe Nearness Of You
Old 97sQuestionThis is taken from the moment when Ed proposes to Carol in Ed (obviously!)
OneRepublicGood Life
Paul McCartneyNo More Lonely Nights
Peter BestEcho BillabongI’m not ashamed to say that Linda Kozlowski in a swimsuit had something to do with this…!
Peter GabrielBiko
Peter GabrielIn Your EyesCameron Fairchild, where are you now?! I met him in Amarillo, TX, and we were best friends for a few months during my year off. He was a fan of Peter Gabriel, and we played Risk, Axis & Allies and Conquest of Empire until the early hours before retiring to Denny’s for the all-day (and all-night!) breakfast…
Peter GabrielRed Rain
Peter GabrielSolsbury Hill
Peter GabrielMercy Street
Peter GabrielBook Of Love
Peter Gabriel & Kate BushDon’t Give Up
PoguesLove You ‘Til The End
Pointer SistersJump (For My Love)
PretendersHumanThis is the theme from Cupid with Jeremy Piven and Paula Marshall, the best TV show never to be given a full season
PucciniO Mio Babbino CaroI have to admit I heard this first on the soundtrack to A Room with a View, but they certainly picked the right version and the right soprano to sing it!
PucciniChi Il Bel Sogno Di DorettaAgain from A Room with a View, and I almost prefer this aria now
PucciniNessun DormaI had a friend Pete Bouman at Oxford, who was an exchange student passionate about opera. One day in his rooms, he tried to play me an aria in which a soprano hit top C, but while he was fumbling with the fast forward and rewind buttons I heard this wonderful classic and made him play it for me. An early taste of Italia ’90!
RachmaninovRhapsody on a Theme of PaganiniGroundhog Day is my favourite film ever, and this music has an important part to play!
Rachmaninov2nd Piano Concerto, Mvt 1Who but the most cynical of viewers could fail to be moved to tears by the score of Brief Encounter (even if my mother happened to catch me…!)?
Rachmaninov2nd Piano Concerto, Mvt 2
Rachmaninov2nd Piano Concerto, Mvt 3
Ray CharlesWhat’d I Say
Remy ZeroFair
Remy ZeroSave MeThis one’s from Smallville. US teen dramas don’t get any cornier (so to speak…)
Rolling StonesGimme Shelter
Rolling StonesStart Me Up
Rolling StonesSympathy For The DevilI was once at a party with Damian Hinds, who insisted on playing this even though nobody could dance to it!
Rolling StonesWild HorsesVicki again. Sigh…
Run DMC & AerosmithWalk This WayThis was the soundtrack to my very first race off the lights in Amarillo, TX. Eighty miles an hour, top down all the way. Glory…
Sam FonteynPop Looks Bach
Sarah McLachlanPossession
ScorpionsWind Of Change
SemisonicClosing Time
Sinead LohanNo Mermaid
Sixpence None The RicherKiss Me
Sixpence None The RicherThere She Goes
Smashing Pumpkins1979
Steve ReynoldsHouse I Built
StiltskinInsideWhat a great Levi jeans advert! The music and pictures were in perfect harmony. Amish girl in black and white plus heartthrob and rock music – sounds like Witness!
T RexCosmic DancerFrom the soundtrack to Billy Elliot
Take ThatBack for Good (Radio Mix)
ToploaderDancing In The MoonlightAnyone who went to Bananas in Val d’Isere around midnight would remember this one (and Angel by Robbie Williams)!
TrainDrops Of JupiterStand up, Craig Campbell. I only managed to make you dinner once that season in Mottaret, but we told so many stories while listening to so many songs that I have to credit you with the inspiration for this post!
Trespassers WilliamLie In The Sound
Trevor Jones & Randy EdelmanAscent/PursuitFrom The Last of the Mohicans. Definitely a better film than the book!
Trevor Jones & Randy EdelmanLast Of The Mohicans (Main Theme)
U2Walk On
U2Where The Streets Have No NameThis is the theme to the promotional video of the Gnat Display Team, which I managed for a while in 2010-11
U2Who’s Gonna Ride Your Wild Horses
Vanessa CarltonA Thousand Miles
VerdiDammi Tu Forza, O Cielo!Julia Roberts ‘peed her pants’ to this in Pretty Woman. What more can you say?!
WaterboysThe Whole Of The Moon
WhoBaba O’Reilly
WhoThe Seeker
YazooOnly You