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Question
l is the perpendicular bisector of line segment PQ and R is a point on the same side of l as P. The segment QR intersects l at X. Prove that PX + XR = QR.
Solution
Since, line 1 is the perpendicular bisector of PQ and X lies on 1. Therefore, X is equidistant from P and Q.
i.e., PX = QX
⇒ PX + XR = QX + XR
⇒ PX + XR = QR.
Hence proved.
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