Question

Q.4.A) Solve the following (Any-2)
1) The radius of the circle is 13 cm The length of a chord is 10 cm,
Find the distance of the chord/from the centre of the circle
2) If the measure of a central angle is 120".
find the measure of corresponding minor are​

Answer 1

Answer:

12 cm

Step-by-step explanation:

Let AB be a chord of a circle with centre O and radius 13 cm such that AB = 10 cm.

From O, draw OL ⊥ AB. Join OA.

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

∴ AL = LB = ½ AB = 5 cm

Now, in right triangle OLA, we have

OA2 = OL2 + AL2

⇒ 132 = OL2 = 52

⇒ 132 – 52 = OL2

⇒ OL2 = 144

⇒ OL = 12 cm.

Hence, the distance of the chord from the centre is 12 cm.