Question

In the adjoining figure, seg MN is a chord of a circle with centre O. MN = 25, L is a point on chord MN such that ML = 9 and d(0, L) = 5. Find the radius of the circle.

Construction: Draw seg OK ⊥ chord MN. Join OM.

Answer 1

seg OK ⊥ chord MN [Construction]

∴ MK = 1/2 MN [Perpendicular drawn from the centre of the circle to the chord bisects the chord]

= 1/2 × 25

= 12.5 units

MK = ML + LK [M – L – K]

= 13 units [Taking square root of both sides] 

∴ The radius of the given circle is 13 units.