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in which ines are drawn through A, B and C paralial to the sidesBC, CA and AB respectively forming APOR. Show that BC- 1QR.2 |
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Answer» Given In ΔABC, PQ || AB and PR || AC and RQ || BC.To show BC = 1/2 QRProof In quadrilateral BCAR, BR || CA and BC|| RASo, quadrilateral, BCAR is a parallelogram.BC = AR …(i)Now, in quadrilateral BCQA, BC || AQand AB||QCSo, quadrilateral BCQA is a parallelogram,BC = AQ …(ii)On adding Eqs. (i) and (ii), we get2 BC = AR+ AQ⇒ 2 BC = RQ⇒ BC = 1/2 QRNow, BEDF is a quadrilateral, in which ∠BED = ∠BFD = 90°∠FSE = 360° – (∠FDE + ∠BED + ∠BFD) = 360° – (60° + 90° + 90°)= 360°-240° =120° |
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