Geometry-Angles in a Circle

Front

What is the measure of an angle formed by a diameter and a point on the circle?

Back

90°

Tags

CCSS.HSG.C.A.2

Front

If two arcs of a circle are given, how do you find the measure of the angle formed by a tangent and a secant intersecting outside the circle?

Back

The measure of the angle is half the difference of the measures of the intercepted arcs.

Tags

CCSS.HSG.C.A.2

Front

In a cyclic quadrilateral, what is the relationship between opposite angles?

Back

The sum of the measures of opposite angles is 180°.

Tags

CCSS.HSG.C.A.2

Front

How do you calculate the measure of an angle formed by two intersecting chords inside a circle?

Back

The measure of the angle is half the sum of the measures of the intercepted arcs.

Tags

CCSS.HSG.C.A.2

Front

What is the relationship between the measure of an arc and the angle subtended by it at the center of the circle?

Back

The measure of the angle at the center is equal to the measure of the arc.

Tags

CCSS.HSG.C.B.5

Front

If arc AB measures 70° and angle AOB is formed at the center, what is the measure of angle AOB?

Back

70°

Tags

CCSS.HSG.C.A.2

Front

What is the measure of an angle formed by a tangent and a chord through the point of contact?

Back

The measure of the angle is equal to the measure of the opposite arc.

Tags

CCSS.HSG.C.A.2

Front

If the measure of arc AC is 72° and arc CD is 132°, how do you find the angle formed by a tangent and a secant?

Back

The angle is half the difference of the measures of the arcs: (132° - 72°) / 2 = 30°.

Tags

CCSS.HSG.C.A.2

Front

What is the measure of an angle formed by two secants intersecting outside a circle?

Back

The measure of the angle is half the difference of the measures of the intercepted arcs.

Tags

CCSS.HSG.C.A.2

Front

If m∠A = 95° in a cyclic quadrilateral ABCD, what can be concluded about m∠C?

Back

m∠C = 85° (because m∠A + m∠C = 180°).

Tags

CCSS.HSG.C.A.2