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right triangle, incircle and circumcircle related 2017 BMT Team 9

Source:

January 5, 2022
geometryright triangle

Problem Statement

Let AB=10AB = 10 be a diameter of circle PP. Pick point CC on the circle such that AC=8AC = 8. Let the circle with center OO be the incircle of ABC\vartriangle ABC. Extend line AOAO to intersect circle PP again at DD. Find the length of BDBD.