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O is a point on side PQ of a APQR such that PO = QO = RO, then(a) RS² = PR × QR(b) PR² + QR² = PQ²(c) QR² = QO² + RO²(d) PO² + RO² = PR² |
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Answer» In ΔPQR , PO=OQ=RO (given) Now , in ΔPSR , PO=OR (given) ∴∠1=∠P [Angles opposite to equal sides in a triangle are equal] Similarly , in ∠ORQ , RO=OQ (given) ∠Q=∠2 Now , in ΔPQR , ∠P+∠Q+∠PRQ=180∘ [By Angle sum property of a triangle] ⇒∠1+∠2+(∠1+∠2)=180∘ ⇒2(∠1+∠2)=180∘ ⇒∠1+∠2=90∘ ⇒∠PRQ=90∘ By Pythagoras theorem , we have PQ2=QR2+PQ2 option B is correct |
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