In a trapezoid ABCD, the internal bisector of angle A intersects the base BC (or its extension) at t

Question

In a trapezoid ABCD, the internal bisector of angle A intersects the base BC (or its extension) at the point E. Inscribed in the triangle ABE is a circle touching the side AB at M and side BE at the point P. Find the \angle DAE in degrees, if AB : MP = 2.

Accepted Answer

{"content":[{"content":[{"marks":[{"type":"bold"}],"text":"Step 1:","type":"text"},{"text":" Given, PM ","type":"text"}],"type":"paragraph"},{"type":"paragraph","content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step 2:"},{"text":" ∠BAE = ∠AEB = ","type":"text"}]},{"content":[{"marks":[{"type":"bold"}],"text":"Step 3:","type":"text"},{"text":" By symmetry M is mid-point of BA","type":"text"}],"type":"paragraph"},{"type":"paragraph","content":[{"marks":[{"type":"bold"}],"text":"Step 4:","type":"text"},{"text":" =>         y => xy","type":"text"}]},{"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step 5:"},{"type":"text","text":" =>    ∠B = 60° => ∠A = 60°"}],"type":"paragraph"}],"type":"doc"}

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