Question

AB = 16 cm, OM = 15 cm, ON = 8 cm

radius =

Options

• 20 cm

• 25 cm

• 17 cm

• 30 cm

Answer 1

17 cm

Explanation:

Given:

• AB = 16 cm(the length of the chord.
• OM = 15 cm the perpendicular distance from the center O to the midpoint M of the chord AB.
• ON = 8 cm distance from O to N, another point on the radius.

Let r be the radius of the circle, which is the hypotenuse of the right-angled triangle formed by:

1. Half the length of the chord AB, which is `16/2` = 8 cm.
2. The perpendicular distance from the center to the chord OM = 15 cm.

Using the Pythagorean theorem:

`r^2 = OM^2 + ((AB)/2)^2`

r² = 15² + 8²

r² = 225 + 64 = 289

r = `sqrt(289)`

r = 17 cm

Thus, the radius of the circle is 17 cm.