10.5 Angle Relationships in Circles

Front

What is the measure of an angle formed by two tangents drawn from a point outside a circle?

Back

The measure of the angle formed by two tangents drawn from a point outside a circle is equal to half the difference of the measures of the intercepted arcs.

Tags

CCSS.HSG.C.A.2

Front

What is the relationship between the angles formed by two chords that intersect inside a circle?

Back

The measure of each angle formed by two intersecting chords is equal to half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

Tags

CCSS.HSG.C.A.2

Front

How do you find the measure of an arc in a circle?

Back

The measure of an arc can be found by using the central angle that subtends the arc, where the measure of the arc is equal to the measure of the central angle.

Tags

CCSS.HSG.C.B.5

Front

What is the relationship between the angles formed by a tangent and a chord?

Back

The measure of the angle formed by a tangent and a chord through the point of contact is equal to half the measure of the intercepted arc.

Tags

CCSS.HSG.C.A.2

Front

What is the formula to find the measure of an angle formed by two secants that intersect outside a circle?

Back

The measure of the angle formed by two secants that intersect outside a circle is equal to half the difference of the measures of the intercepted arcs.

Tags

CCSS.HSG.C.A.2

Front

What is the measure of an inscribed angle in a circle?

Back

The measure of an inscribed angle is equal to half the measure of the intercepted arc.

Tags

CCSS.HSG.C.A.2

Front

What is the relationship between the measures of arcs and angles in a circle?

Back

The measure of an angle is often related to the measures of the arcs it intercepts, with specific relationships depending on whether the angle is inscribed, central, or formed by tangents.

Tags

CCSS.HSG.C.A.2

Front

How do you solve for x in an equation involving angles in a circle?

Back

To solve for x in an equation involving angles in a circle, set up the equation based on the relationships between the angles and arcs, and then isolate x.

Tags

CCSS.HSG.C.A.2

Front

What is the significance of the central angle in relation to the arcs it subtends?

Back

The central angle is significant because it directly determines the measure of the arc it subtends, being equal in measure.

Tags

CCSS.HSG.C.B.5

Front

What is the formula for the sum of the measures of the angles formed by intersecting chords?

Back

The sum of the measures of the angles formed by intersecting chords is equal to the sum of the measures of the arcs intercepted by those angles.

Tags

CCSS.HSG.C.A.2