## What is the relation of inscribed angle and its intercepted arc?

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## What is the relation of inscribed angle and its intercepted arc?

Theorem 70: The measure of an inscribed angle in a circle equals half the measure of its intercepted arc.

## What seems to be the relationship inscribed angle and its intercepted arc How about central angle and inscribed angle?

The measure of the inscribed angle is half the measure of the arc it intercepts. If a central angle and an inscribed angle intercept the same arc, then the central angle is double the inscribed angle, and the inscribed angle is half the central angle.

What is relationship between arcs and inscribed angles of a circle?

Inscribed angles are angles whose vertices are on a circle and that intersect an arc on the circle. The measure of an inscribed angle is half of the measure of the intercepted arc and half the measure of the central angle intersecting the same arc. Inscribed angles that intercept the same arc are congruent.

### What is inscribed angle in a circle?

An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of a circle. This is different than the central angle, whose vertex is at the center of a circle. If you recall, the measure of the central angle is congruent to the measure of the minor arc.

### What are the relationships between inscribed central and circumscribed angles of a circle?

-A circumscribed angle is created by two intersecting tangent segments. -The measure of a central angle will be twice the measure of an inscribed angle that intercepts the same arc.

What is intercepted arc in a circle?

An intercepted arc is a portion of the circumference of a circle encased by two line segments meeting at a vertex, or center of the circle.

#### How do you solve inscribed arcs?

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°.

#### How are angles and intercepted arcs of circles related and applied?

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.