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
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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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