Proposed Problem

Click the figure below to see the complete problem 350 about Triangle, Cevian, Incircles, Tangents, Tangency Points, Angles.

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Complete Problem 350

Level: High School, SAT Prep, College geometry

## Friday, August 28, 2009

### Problem 350. Triangle, Cevian, Incircles, Tangents, Angles,Tangency Points

Labels:
angle,
cevian,
circle,
common tangent,
incircle,
tangency point,
tangent,
triangle

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Problem 350 solution: This solution was submitted by Michael Tsourakakis from Greece

ReplyDeleteThanks Mixalis.

Per the result of problem 349 we have GE=RM

ReplyDeleteWe have BG=BM

BR=BM-RM

But BM=BG and RM= EG so BR= BE

So BE=BR=BT

And B is the center of circumcircle of triangle ERT

So central angle ABD= 2 x inscribed angle ETR