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TS _|_ SE if SA = SP and TB = TD

Source: 2th XMO (China) Test 2 p1 https://artofproblemsolving.com/community/c3192772_geometry_regional_china

April 7, 2024
geometryperpendicular

Problem Statement

As shown in the figure, BQBQ is a diameter of the circumcircle of ABCABC, and DD is the midpoint of arc BCBC (excluding point AA) . The bisector of the exterior angle of ∠BAC\angle BAC intersects and the extension of BCBC at point EE. The ray EQEQ intersects ⊙(ABC)\odot (ABC) at point PP. Point SS lies on PQPQ so that SA=SPSA = SP. Point TT lies on BCBC such that TB=TDTB = TD. Prove that TS⊥SETS \perp SE. https://cdn.artofproblemsolving.com/attachments/c/4/01460565e70b32b29cddb65d92e041bea40b25.png
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