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QR =\perp AD in orthodiagonal isosceles trapezoid (2011 Romania District VII P2)

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May 19, 2020
geometrytrapezoidperpendiculardiagonals

Problem Statement

The isosceles trapezoid ABCDABCD has perpendicular diagonals. The parallel to the bases through the intersection point of the diagonals intersects the non-parallel sides [BC][BC] and [AD][AD] in the points PP, respectively RR. The point QQ is symmetric of the point PP with respect to the midpoint of the segment [BC][BC]. Prove that:
a) QR=ADQR = AD, b) QR⊥ADQR \perp AD.
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