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Three circles share a common point

Source: 2022 China Southeast Grade 11 P6

August 3, 2022
geometry

Problem Statement

Let OO be the circumcenter of △ABC\triangle ABC. A circle with center PP pass through AA and OO and OPOP//BCBC. DD is a point such that ∠DBA=∠DCA=∠BAC\angle DBA = \angle DCA = \angle BAC. Prove that: Circle (P)(P), circle (BCD)(BCD) and the circle with diameter (AD)(AD) share a common point. https://services.artofproblemsolving.com/download.php?id=YXR0YWNobWVudHMvMS9jLzlmZjdlN2ExZDJjYjAwYWJlZTQzYWRkYzg3NDlhMTUyZjRlNGJjLmpwZw==&rn=c291dGhlYXN0UDYuanBn
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