Proposed Problem

Click the figure below to see the complete problem 437 about Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement.

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Complete Problem 437

Level: High School, SAT Prep, College geometry

## Sunday, April 25, 2010

### Problem 437: Tangent Circles, Diameter, Chord, Perpendicular, Congruence

Labels:
chord,
circle,
congruence,
diameter,
measurement,
perpendicular,
similarity,
tangent

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▲ANE ~ ▲AMH => AN/AM = AE/AH (1)

ReplyDelete▲AFE ~ ▲AGH => AF/AG = AE/AH = AC/AB (2)

from (1) & (2)

AN/AM = AC/AB

(3)

PK perpendic to AB

▲APK ~ ▲ADE => AP/AD = AC/AB (4)

from (3) & (4)

AN/AM = AP/AD ( AM = AD from P436 )

AN = AP

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AN.AM = AE.AC, CENM being concyclic

ReplyDeleteAM^2 = AE.AB

Dividing, AN/AM = AC/AB = AP/AD since CP//BD

Since AD = AM as proved in Problem 436, AP = AN

Sumith Peiris

Moratuwa

Sri Lanka