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Step-by-step explanation:
This problem can be solved by using the concept of similarity of the triangles.
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=> HOPE IT HELPS YOU SIS...
Given that X divides PQ in 2:1
= QX = 2/3 × PQ -----(1)
Similarly, Y divides QR in 2:1
= RY = 2/3 × QR -----(2)
In ∆PYQ,
PY² = PQ² + QY²
PY² = PQ² + (2/3 × QR)²
9PY² = 9PQ² + 4QR² ----(3)
In ∆XQR,
XR² = XQ² + QR²
XR² = (2/3 × PQ)² + QR²
XR² = 4/9 × PQ² + QR²
9XR² = 4PQ² + 9QR² ----(4)
On adding (3)+(4), we get
9(PY² + XR²) = 13(PQ² + QR²)
9(PY² + XR²) = 13PR² hence proved..
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