Home Geometry Problems All Problems 341-350 View or post a solution 
Problem 350. Triangle, Cevian, Incircles, Tangents, Tangency Points, Angles. Level: High School, College, SAT Prep.

The figure shows a triangle ABC with point D on side AC. Circles 1, 2, and 3 are the incircles of triangles ABC, ABD, and BDC, respectively. QS is the common tangent to circles 2 and 3. QS intersects to cevian BD at R. If E,G,H,F,P,N,M,Q,S, and T are points of tangency, prove that the angle ABD is double the angle ETR.
 

Triangle, Cevian, Incircles, Angles 

 


 

Geometry problem solving is one of the most challenging skills for students to learn. When a problem requires auxiliary construction, the difficulty of the problem increases drastically, perhaps because deciding which construction to make is an ill-structured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given."

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