What is the intercepted arc of an inscribed angle?

What is the intercepted arc of an inscribed angle?

The intercepted arc is the arc that is inside the inscribed angle and whose endpoints are on the angle. The vertex of an inscribed angle can be anywhere on the circle as long as its sides intersect the circle to form an intercepted arc.

What is the relationship between inscribed angle and intercepted arc?

The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc. Inscribed angles that intercept the same arc are congruent.

What conjecture can you draw from the measures of inscribed angle and its intercepted arc?

Corollary (Inscribed Angles Conjecture II ): In a circle, two inscribed angles with the same intercepted arc are congruent. Proof: The measure of each inscribed angle is exactly half the measure of its intercepted arc. Since they have the same intercepted arc, they have the same measure.

How do you solve an inscribed angle?

By the inscribed angle theorem, the measure of an inscribed angle is half the measure of the intercepted arc. The measure of the central angle ∠POR of the intercepted arc ⌢PR is 90°. Therefore, m∠PQR=12m∠POR =12(90°) =45°.

Which is an inscribed angle?

In geometry, an inscribed angle is the angle formed in the interior of a circle when two chords intersect on the circle. It can also be defined as the angle subtended at a point on the circle by two given points on the circle.

What is the relationship between inscribed angle and central angle?

The measure of the central angle is the same measure of the intercepted arc. You can see that if a central angle and an inscribed angle intercept the same arc, the central angle would be double the inscribed angles. Likewise, the inscribed angle is half of the central angle.

What is the relationship among arcs central angles and inscribed angles?

A chord of a circle is a line segment whose endpoints lie on the circle. An inscribed angle is the angle formed by two chords having a common endpoint. The other endpoints define the intercepted arc. The central angle of the intercepted arc is the angle at the midpoint of the circle.

Why is inscribed angle theorem true?

The inscribed angle theorem states that an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle. Therefore, the angle does not change as its vertex is moved to different positions on the circle.

Which arc is intercepted by angle PQR?

arc PTR is intercepted by ∠PQR.