Geometry Problem

Level: Mathematics Education, High School, Honors Geometry, College.

Click the figure below to see the complete problem 687.

## Wednesday, November 9, 2011

### Problem 687: Triangle, Excircles, Tangency points, Tangent lines, Concurrent Lines

Labels:
concurrent,
excircle,
tangency point,
tangent,
triangle

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Let A’, B’, C‘ are contacting points of encircles to BC, AC and AB

ReplyDeletePer the result of problem 682, 3, B3 and C3 are Gergonne points

AA3 will cut BC at A’ and A’B/A’C= (s-a)/(s-b)

Similarly B’C/B’A=(p-a)/p-c) and C’A/C’B=(s-b)/(s-a)

And A’B/A’C . B’C/B’A . C’A/C’B = 1

So AA3, BB3 and CC3 are concurrent per Ceva’s Theorem

Peter Tran

Typos:

ReplyDeleterhs's of

A’B/A’C= (s-a)/(s-b),

B’C/B’A=(p-a)/p-c)and

C’A/C’B=(s-b)/(s-a)

to be corrected as

(s-c)/(s-b),

(s-a)/(s-c)and

(s-b)/(s-a)respectively