Question

Pbe a point inside a circle having centre O and radius 10 cm. If OP = 4 and APB be a chord of circle through P, then find the value of PA PB.​

Answer 1

Given info : P be a point inside a circle having centre O and radius 10 cm. If OP = 4 and APB be a chord of circle through P.

To find : the value of PA and PB.

solution : we know, a line drawn from centre of circle is the perpendicular bisector of chord.

so, OP is perpendicular bisector of AB.

now, ∆OPB [ see figure ]

from Pythagoras theorem,

OB² = OP² + PB²

⇒(10cm)² = (4cm)² + PB²

⇒100 - 16 = PB²

⇒PB² = 84

⇒PB = 2√21 cm

∵ PA = PB [ OP divided chord into two equal parts ]

Therefore, PA = PB = 2√21 cm