Question

In the following figure, point O is the centre of the circle and length of chord AB is equal to the radius of the circle. Find the measures of:

a. ∠AOB

b. arc AB

c. ∠ACB

by completing the activity.

Activity:

In ΔAOB,

AO = OB = AB

∴ ΔAOB is an `square` triangle.

∴ m∠AOB = `square`

∴ m∠AOB = m(arc AB) = `square`   ...(Definition of measure of an arc)

m∠ACB = `1/2 xx  square`   ...`square`

= `1/2 xx 60^circ`

m∠ACB = `square`

Answer 1

Activity:

In ΔAOB,

AO = OB = AB

∴ ΔAOB is an \[\boxed{\text{equilateral}}\] triangle.

∴ m∠AOB = \[\boxed{60°}\]

∴ m∠AOB = m(arc AB) = \[\boxed{60°}\]   ...(Definition of measure of an arc)

\[\text{m∠ACB} = \frac{1}{2} \times \boxed{\text{m(arc AB)}}\]   ...\[\boxed{\text{Inscribed angle theorem}}\]

= `1/2 xx 60^circ`

m∠ACB = \[\boxed{30°}\]