Geometry Problem

Click the figure below to see the complete problem 457 about Triangle, First Brocard Point, Congruent angles, Circle, Circumradius.

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Complete Problem 457

Level: High School, SAT Prep, College geometry

## Tuesday, May 18, 2010

### Problem 457: Triangle, Brocard Point, Congruent angles, Circle, Circumradius

Labels:
angle,
Brocard Point,
circumcircle,
circumradius,
congruence,
measurement,
triangle

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in triangle ABC

ReplyDeletea/sinA=b/sinB=c/sinC=2R

abc/(sinA.sinB.sinC)=8R^3

in triangle APC

ang(APC)=180-C

b/sin(180-C)=b/sinC=2e

in triangle BPC

ang(BPC)=180-B

a/sinB=2d

in triangle BPA

ang(BPA)=180-A

c/sinA=2f

hence abc/(sinA.sinB.sinC)=8def=8R^3

R^3=def

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