Question

6. Let
ot, figure, in a circle with centre 0, length
chord AB is equal to the radius of the
circle. Find the measure of each of the
following:
(1) ZAOB
(2) ZACB
(3) arc AB
(4) arc ACB.
​

Answer 1

$\huge \underline\mathbb \purple {ANSWER :} \over$

(1)

In the given figure, OA and OB are the radii of the circle.

OA = OB = AB (Given)

∴ ∆OAB is an equilateral triangle.

⇒ ∠AOB = ∠OAB = ∠OBA = 60º

Thus, the measure of ∠AOB is 60º.

─────────────────────

(2)

The measure of an angle subtended by an arc at a point on the circle is half of the measure of the angle subtended by the arc at the centre.

∠ACB = 12∠AOB = 12×60° = 30º

Thus, the measure of ∠ACB is 30º.

─────────────────────

(3)

m(arc AB) = ∠AOB = 60º (Measure of an arc is the measure measure of its corresponding central angle)

Thus, the measure of arc AB is 30º.

─────────────────────

(4)

m(arc ACB) = 360º − m(arc AB) = 360º − 60º = 300º

Thus, the measure of arc ACB is 300º.

===============================