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PO _|_BC wanted, circle passing thorugh A,C and tangent to median AM

Source: China Northern MO 2013 p6 CNMO

October 28, 2022
perpendiculargeometry

Problem Statement

As shown in figure , it is known that MM is the midpoint of side BCBC of △ABC\vartriangle ABC. ⊙O\odot O passes through points A,CA, C and is tangent to AMAM. The extension of the segment BABA intersects ⊙O\odot O at point DD. The lines CDCD and MAMA intersect at the point PP. Prove that PO⊥BCPO \perp BC. https://cdn.artofproblemsolving.com/attachments/8/a/da3570ec7eb0833c7a396e22ffac2bd8902186.png
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