Question

AB is a chord of circle with centre O. At B, a tangent PB is drawn such that its length is 24 cm. The distance of P from the centre is 26 cm. If the chord AB is 16 cm, find its distance from the centre.

Answer 1

We need to find the distance of chord from the centre if the chord AB is 16 cm. On joining OB and drawing OC ⊥ AB, the figure can be drawn as shown below

From ∆OBP, on using Pythagoras  theorem, we get

OP² = OB² + BP²

On substituting the values, we get

⇒ 26² = OB² + 24²

⇒ 676 = OB² + 576

⇒ OB² = 100

⇒ OB = 10 cm

It is known that the perpendicular drawn from the centre to the chord, divides the chord into two equal parts. Hence, BC = 8 cm

Similarly, from ∆OBC, on using Pythagoras theorem, we get

OB² = OC² + BC²

On substituting the values, we get

⇒ 10² = OC² + 8²

⇒ 100 = OC² + 64

⇒ OC² = 36

⇒ OC = 6 cm

Hence, the distance of the chord from the centre is 6 cm.

Answer 2

Given, AB is a chord of circle with centre O and tangent PB = 24, OP = 26 cm.