Question

O and C are centres of the two circles. The 2 radii are 15 cm and 13 cm. If AB = 24 cm. The length of OC is ______.

पर्याय

• 10 cm

• 17 cm

• 15 cm

• 14 cm

Answer 1

O and C are centres of the two circles. The 2 radii are 15 cm and 13 cm. If AB = 24 cm. The length of OC is 14 cm.

Explanation:

Step 1:

The common chord AB is bisected by the line connecting the centers OC.

Let M be the midpoint of AB.

`AM = (AB)/2`

= `24/2`

= 12 cm

Step 2:

In right triangle OMA, OA is the radius of the first circle (r₁ = 15 cm).

OM² = OA² – AM²

OM² = 15² – 12²

= 225 – 144

= 81

OM = `sqrt(81)` = 9 cm

Step 3:

In right triangle CMA, CA is the radius of the second circle (r₂ = 13 cm).

CM² = CA² – AM²

CM² = 13² – 12²

= 169 – 144

= 25

CM = `sqrt(25)` = 5 cm

Step 4:

The distance between the centers OC is the sum of OM and CM.

OC = OM + CM

= 9 + 5

= 14 cm