A geometry problem by sujoy roy
ABC is an isosceles triangle with AB=AC and
.
P is a point inside the triangle such that
and
. Find
.
Note: Use only geometry to solve the problem.
The answer is 110.
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1 solution
Denote: A H ⊥ B C , A H × B P = I , ∠ B I H = ∠ C I H = 6 0 0 ⇒ IP is the bisector of angle AIC, beside PC is the bisector of angle ACI. P is the incenter of triangles ACI, AP is the bisector of the angle IAC. ⇒ ∠ A P B = 1 8 0 0 − ( 4 0 0 + 3 0 0 ) = 1 1 0 0