Question

AB is diameter of circumcircle triangle APB. N is foot of perpendicular from P on AB if AP=8cm and PB=6cm then find length of BN

Answer 1

As per Question we have angle P is 90 degree
AB²=AP² + PB²=64=36=100
⇒ AB=10cm
Let BN = X cm
From triangle APN we have PN² = AP² - AN²
From triangle PNX we have PN² = PB² - X²
we have PB² - X² = AP² - AN²
                   ⇒  6² - X² = 8² - (10-X)²
                   ⇒   36 - X² = 64-100-X² + 20X
                   ⇒    20 X =  72
                               X = 3.6
  length of BN =3.6