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State the dual of the Theorem below. Let a non-degenerate plane conic touch the sides BC,...

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Advance Math

State the dual of the Theorem below.

Let a non-degenerate plane conic touch the sides BC, CA, and ABof a triangle ABC in R2 at the points P, Q, and Rrespectively. Then AP, BQ, and CR are concurrent.

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Answer Let T be the intersection of the circumcircles of ARQ and BP R By collinearity of points T QA CQT T RB ART T P C BP T In a cyclic quadrilateral opposite angles are supplementary Therefore T QA ART T RB BP T We conclude T P C CQT Now conversely a    See Answer
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