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Q1 of 62 Page 10

The radius of a circle is 13 cm and length of one of its chords is 24 cm. Find the distance of the chord from the centre.

Let AB = 24 cm be the chord of the circle with radius AO = 13 cm.
Draw OP ⊥ AB. Join OA according to theorem,
AP=

휤 = 12 cm
In Δ APO, ∠P = 90°
.^.. AO²= AP²+ OP²
= 12²+ OP²
⇒ 13²= 12²+ OP²
⇒ OP = 5 cm

More from this chapter

2 AB and CD are two parallel chords of a circle such that AB = 10 cm and CD = 24 cm. If chords are on opposite sides of the centre of the circle and distance between them is 17 cm find the radius of the circle.

3 Determine the length of a chord, which is at a distance of 5 cm from the centre of the circle of radius 13 cm.

4 In the Fig. AB and AC are two equal chords of a circle. Prove that bisector of ∠BAC passes through the centre of the circle.

5 In the adjoining figure, OD is perpendicular to the chord AB of a circle whose centre is O. If BC is a diameter, show that AC = 2 OD and AC ||OD.