Question

A chord of length 30 cm is drawn in a circle of radius 17 cm. Find its distance from the centre of the circle.

• A. 12 cm
• B. 10 cm
• C. 8 cm
• D. 6 cm

Answer 1

The correct option is C

8 cm

Chord AB = 30 cm, radius OA = 17 cm.

From O, draw OL$\perp$AB. Join OA.

Since, perpendicular drawn from the centre of circle to a chord biscets the chord.

Hence, AL = $\frac{AB}{2}$ = $\frac{30}{2}$ = 15 cm.

In right-angled $\Delta$OLA, we have

OL = $\sqrt{\left({OA}^2\right)-\left({AL}^2\right)}$ = $\sqrt{\left({17}^2\right)-\left({15}^2\right)}$ = $\sqrt{\left(289\right)-\left(225\right)}$ = $\sqrt{\left(289\right)-\left(225\right)}$ = $\sqrt{64}$ = 8 cm.

Hence the distance of the chord from the centre is 8 cm.