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Cute Geometry Problem

Source: BdMO 2023 Higher Secondary National P9

February 12, 2023
geometryparallelcyclic quadrilateralradical axisAngle ChasingInversion

Problem Statement

Let ΔABC\Delta ABC be an acute angled triangle. DD is a point on side BCBC such that ADAD bisects angle ∠BAC\angle BAC. A line ll is tangent to the circumcircles of triangles ADBADB and ADCADC at point KK and LL, respectively. Let MM, NN and PP be its midpoints of BDBD, DCDC and KLKL, respectively. Prove that ll is tangent to the circumcircle of ΔMNP\Delta MNP.
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