The diameter of a circle is AB. Point C is on the circumference. What is the measure of the ∠ACB Class 9

The diameter of a circle is AB. Point C is on the circumference. What is the measure of the ∠ACB Class 9

Question 1.

The diameter of a circle is AB. Point C is on the circumference. What is the measure of the ∠ACB? Explain your reasoning. Class 9

Solution:

Since AB is the diameter, the angle subtended by arc AB at the centre is 180°

∴ ∠AOB = 180°

Since the angle subtended by an arc at the centre of the circle is double the angle subtended by the arc at any point on the circle.

∴ ∠ACB = $\frac{180}{2}=90^{\circ}$

Question 2.

ABCD is a cyclic quadrilateral inscribed in a circle. If ∠A measures 75°, what is the measure of ∠C? If ∠B measures 110°, what is the measure of ∠D? Class 9

Solution:

ABCD is a cyclic quadrilateral

Since the sum of two opposite angles of a cyclic quadrilateral is 180°

∴ ∠A + ∠C = 180°

∴ 75° + ∠C = 180°

∴ ∠C = 105°

Similarly, ∠B + ∠D = 180°

∴ 110° + ∠D = 180°

∴ ∠D = 70°