Question

In the adjoining figure, seg QR is a chord of the circle with centre O. P is the midpoint of the chord QR. If QR = 24, OP = 10, find radius of the circle. To find solution of the problem, write the theorems that are useful. Using them, solve the problem.

Answer 1

Theorems which are useful to find solution:

i. The segment joining the centre of a circle and the midpoint of a chord is perpendicular to the chord. 

ii. In a right angled triangle, sum of the squares of the perpendicular sides is equal to square of its hypotenuse.

\(QP = 1/2 \) (QR) [P is the midpoint of chord QR]

1/2 × 24 = 12 units

Also, seg OP ⊥ chord QR [The segment joining centre of a circle and midpoint of a chord is perpendicular to the chord]

∴ The radius of the circle is 2√61 units.