12.4- Secant Angles

Front

What is a secant angle?

Back

A secant angle is an angle formed by two secant lines that intersect outside a circle.

Front

How do you find the measure of an angle formed by two secants?

Back

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

Front

What is the formula for finding the measure of an angle formed by two secants?

Back

If angle F is formed by secants EA and EB, then m∠F = 1/2 (mArc EA - mArc EB).

Front

What is the measure of arc EA if m∠F = 35° and mArc EB = 129°?

Back

Using the formula: mArc EA = 2 * m∠F + mArc EB = 2 * 35 + 129 = 129°.

Front

If the measure of arc EA is 129°, what is the measure of angle F?

Back

Using the formula: m∠F = 1/2 (mArc EA - mArc EB). If mArc EB is 129°, then m∠F = 1/2 (129 - 129) = 0°.

Front

What is the relationship between secant angles and intercepted arcs?

Back

Secant angles are directly related to the measures of the intercepted arcs, as the angle's measure is derived from the arcs.

Front

How do you calculate the length of a segment formed by two secants?

Back

The length of the segment can be found using the Power of a Point theorem.

Front

What is the Power of a Point theorem?

Back

The Power of a Point theorem states that if a point is outside a circle, the product of the lengths of the two segments from the point to the circle is constant.

Front

If two secants intersect outside a circle, how do you find the length of the segments?

Back

If the lengths of the segments are a and b, and the external segment is c, then a * b = c².

Front

What is the measure of angle ABD if mArc AB = 100° and mArc CD = 50°?

Back

Using the secant angle formula: m∠ABD = 1/2 (mArc AB - mArc CD) = 1/2 (100 - 50) = 25°.