Math, asked by hetal0403, 1 year ago

in the right angke triangle PQR,the perpendicular from R intersects the hypotenuse in D . the bisector of angle R intersects the hypotenuse in E .Then prove that PD/DQ=PE square/EQ square

Answers

Answered by amitnrw
4

PD/DQ =  PE²/EQ²

Step-by-step explanation:

RE is angle bisector of ∠R

=>  PE/EQ  = PR/QR

RD ⊥ PQ  

=> ΔPDR ≈ ΔRDQ

=> PD/RD = PR/RQ  = DR/DQ

=> PD * DQ = DR²

PR² = PD² + RD² = QD² + PD * QD = PD ( PD + QD)

QR² = QD² + RD² = QD² + PD * QD=  QD ( QD + PD)

PR²/QR² = PD ( PD + QD) /  QD ( QD + PD)

=> PR²/QR² =  PD/QD

PR/QR = PE/EQ

=>  PE²/EQ² =  PD/QD

=> PD/DQ =  PE²/EQ²

QED

Proved

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Answered by sruchi17maurya
3

Answer: the answer is with image

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