###### Advertisements

###### Advertisements

O is centre of the circle. Find the length of radius, if the chord of length 24 cm is at a distance of 9 cm from the centre of the circle.

###### Advertisements

#### Solution

Join OA.

Let the perpendicular drawn from point O to the chord AB be P.

We know that the perpendicular drawn from the centre of the circle to the chord bisects the chord.

So, AP = `"AB"/2 = 24/2` = 12 cm

In Δ OPA,

We apply the Pythagoras theorem,

OP² + AP² = OA²

⇒ 9² + 12² = OA²

⇒ OA² = 81 +144 = 225

⇒ OA = √225 15 cm

Hence, the radius of the circle is 15 cm.

#### APPEARS IN

#### RELATED QUESTIONS

In a circle with centre P, chord AB is drawn of length 13 cm, seg PQ ⊥ chord AB, then find l(QB).

Radius of a circle with centre O is 25 cm. Find the distance of a chord from the centre if length of the chord is 48 cm.

C is the centre of the circle whose radius is 10 cm. Find the distance of the chord from the centre if the length of the chord is 12 cm.