Question

The length of the chord AB of the circle with centre O is 8 cm. The perpendicular drawn from O to the chord, intersects the chord at X, and meets the circle at Y. If XY 3 cm, find the radius of the circle.​

Answer 1

Answer:

r = 25/6 cm

Step-by-step explanation:

r = OA

OX = r - 3

Use pythagorean theroem to solve ∆OAX

r^2 = (r - 3)^2 + 4^2

Expand

r^2 = (r^2 - 6r + 9) + 16

Combine like terms

r^2 = r^2 - 6r + 25

Subtract r^2 from both sides

0 = -6r + 25

Add 6r to both sides

6r = 25

Divide both sides by 6

r = 25/6 cm