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Olympiad workbookIOQMProperties of Triangles

In a trapezoid A B C D , the internal bisector of angle A intersects the base B C (or its extension) at the point E . Inscribed in the triangle A B E is a circle touching the side A B at M and side B E at the point P . Find the angle D A E in degrees, if A B: M P=2 .

Correct answer

60

Step-by-step solution

A D | B C Given, P M= x+y 2 aligned & B A E= A E B= & x=z aligned By symmetry M is mid-point of B A array ll & x+y 2 =y x=y & B=60^ A=60^ array

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