Question

The radius of the circle passing through the points (5, 7), (2, -2) and (-2, 0) is ______.

पर्याय

• 2 units

• 5 units

• 3 units

• 4 units

Answer 1

The radius of the circle passing through the points (5, 7), (2, -2) and (-2, 0) is 5 units.

Explanation:

Given, point (5, 7), (2, - 2) and (- 2, 0) lie on circle

Let (h, k) be centre of circle

∴ OA = OC

∴ (h + 2)² + k² = (h - 5)² + (k - 7)²

⇒ h² + 4h + 4 + k²

= h² - 10h + 25 + k² - 14k + 49

⇒ 14h + 14k = 70

h + k = 5   ...(i)

When,OA = OB

∴ (h + 2)² + k² = (h - 2)² + (k + 2)²

⇒ h² + 4h + 4 + k² = h² - 4h + 4 + k² + 4k + 4

⇒ 8h - 4k = 4

2h - k= 1    ...(ii)

From Eqs. (i) and (ii), we get

h = 2, k = 3

∴ Centre of circle (2, 3)

Radius of circle OA = `sqrt((2 + 2)^2 + 3^2)`

OA = `sqrt(4^2 + 3^2)`

`= sqrt(16 + 9)`

`= sqrt25`

= 5 units