Point in a quadrilateral

Geometry Level 2

Given that A B + C D = A D AB + CD = AD and ∠ P A D \angle PAD , ∠ P D A \angle PDA are both bissectors from ∠ B A D \angle BAD and ∠ C D A \angle CDA respectively , is it true that B P = C P BP=CP ?

False True

Relue Tamref by Relue Tamref , 21, Brazil

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1 solution

Relue Tamref
Oct 22, 2017

Let's define a point M M such that A M = A B AM = AB and D M = C D DM = CD by the construction △ A M P ≡ △ A B P \triangle AMP \equiv \triangle ABP by the case angle formed by two equivalent sides A P , A M = A B AP, AM=AB the same for △ D M P \triangle DMP and △ C D P \triangle CDP can be noticed, so we have B P = M P = C P BP = MP = CP

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