Question

in triangle abc if AP is perpendicular to BC and AC square equals to BC square minus AB square then prove that PA square is equals to PB into CP. ​

Answer 1

Answer:

TO PROVE : PA² = BP x PC

Step-by-step explanation:

if  AC² = BC² - AB²

AC² + AB² = BC²

BY CONVERSE OF PYTHAGORAS THEOREM

∠A=90

NOW IN ΔAPB AND ΔABC

∠A=∠APB(90)

∠B = ∠B(COMMON)

BY AA SIMILARITY

ΔAPB≈ΔABC

PA/PB = AB/BC...........(1)

NOW IN ΔABC AND ΔAPC

∠A = ∠APC(90)

∠C=∠C(COMMON)

BY AA SIMILARITY

ΔABC≈ΔAPC

CP/PA = AB/BC ........(2)

EQUAL (1) AND (2)

∴ PA / PB = CP/PA   (BOTH ARE EQUAL TO AB/BC)

∴PA² = PB x PC

HENCE PROVED

Answer 2

Step-by-step explanation:

I hope you got it Thanks......