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BP=CP when AD=AB+CD, angle bisectors related in ABCD (2014 Kyiv City MO 7.4)

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August 5, 2020
geometryangle bisectorequal segments

Problem Statement

In the quadrilateral ABCDABCD the condition AD=AB+CDAD = AB + CD is fulfilled. The bisectors of the angles BADBAD and ADCADC intersect at the point PP , as shown in Fig. Prove that BP=CPBP = CP. https://cdn.artofproblemsolving.com/attachments/3/1/67268635aaef9c6dc3363b00453b327cbc01f3.png
(Maria Rozhkova)
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