Geometry Problem. Post your solution in the comments box below.

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

Click the figure below to see the complete problem 1024.

## Monday, June 16, 2014

### Geometry Problem 1024: Contact, Gergonne Triangle, Point on an arc of Incircle, Perpendicular, Distances

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Denote inscribed angles of arcs PTa, PTc, and TcTb to be a, b, and c respectively.

ReplyDeletea1=PTa*sin(a)=(PTa)^2/(2R)

b1=PTb*sin(b+c)=(PTb)^2/(2R)

c1=PTc*sin(b)=(PTc)^2/(2R)

Plugging these into equation to be proved yields Ptolemy's Theorem in quadrilateral PTaTbTc.