## Friday, April 23, 2010

### Problem 436: Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement.

Proposed Problem
Click the figure below to see the complete problem 436 about Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement.

Complete Problem 436

Level: High School, SAT Prep, College geometry

1. ▲AFE ~ ▲AGH => AF/AG = AE/AH (right tr & comm ang A)
▲AGB ~ ▲AFC => AF/AG = AC/AB (right tr & comm ang A)
=>
AE/AH = AC/AB =>
AB∙AE = AC∙AH =>
(AE + EB)∙AE = (AH+HC)∙AH
AE² + EB∙AE = AH² + HC∙AH
AE² + ED² = AH² + MH² (ED², MH² from euclid Theorem)

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2. Problem 436
APOSTOLIS MANOLOUDIS 4 HIGH SHCOOL OF KORYDALLOS PIRAEUS GREECE

3. By easy angle chase we get tr. ADG ~ tr. AFD and tr. AMG ~ tr. AFM, from their similitude inferring AD^2=AF.AG=AM^2, done

4. Greetings to u all Gogeometers from Sri Lanka as we try to come to terms with what has happened on Easter Sunday

May God help us

< FCA = < GBA = < AGH hence AM^2 = AF.AG

Sumith Peiris
Moratuwa
Sri Lanka

5. Dear Sumith,
My deepest condolences to you and your country

1. Thank u Antonio for your concern.

My wife and I were on the way to churches 100 km North of Colombo when the news came. Pls pray for us.

6. Dear Sumith

My condolences to your country. I remember these victims in my prayers

Peter tran ,
California, usa

1. Thank u very much Peter, really appreciate.