Question

Inscribed shapes

Angle C is inscribed in circle O.
AB is a diameter of circle O.
What is the measure of ZA?

Answer 1

Measure of ZA =
`90^(o)`

Explanation:

Given: A circle O with AB as diameter. Angle C is inscribed in the circle.

To Find: Measure of ZA.

Solution: AB is a diameter.

∴ Measure of AB =
`180^(o)`

∴ ∠C =
`90^(o)` (Inscribed Angle Theorem)

Measure of ZA =
`90^(o)` (Inscribed angle as well as angle in the same segment of the circle.

Inscribed Angle Theorem: Angle subtended by an arc at the center is double the angle subtended by it at any point on the circumference.

Angle in the Same Segment: Angles in the same segment of the circle are equal.

Angle in a Semi-Circle: An angle in a semi-circle is a right angle.