Question

O is the centre of the circle, and AB is a chord. P is a point on AB. PA=3 centimeters, PB-8 centimeters, OP= 5 centimeters what is the radius of the circle?

• A. 5.5 centimeters
• B. 7 centimeters
• C. 5 centimeters
• D. 6.5 centimeters

Answer 1

Answer:

B. 7 centimeters

Extend OP to CD

OD = OC = r = radius of the circle

We know that

PA × PB = PC × PD

3 × 8 = (r - 5)(r + 5)

24 = r² - 5²

24 + 25 = r²

r² = 49

r = 7