Angles formed by chords, secants and tangents

Front

What is the measure of an angle formed by two chords intersecting inside a circle?

Back

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

Front

If arc AB = 80° and arc CD = 40°, what is the measure of angle E?

Back

Angle E = \frac{1}{2}(80° + 40°) = 60°.

Front

What is the relationship between the angle formed by a tangent and a chord through the point of contact?

Back

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

Front

If a tangent intersects a circle at point P and a chord intersects at point Q, how do you find the angle formed?

Back

Angle = \frac{1}{2} \times \text{measure of arc PQ}.

Front

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

Back

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

Front

If arc XY = 120° and arc ZW = 60°, what is the measure of angle A?

Back

Angle A = \frac{1}{2}(120° - 60°) = 30°.

Front

Define a secant in relation to a circle.

Back

A secant is a line that intersects a circle at two points.

Front

What is the formula for finding the angle formed by two intersecting chords?

Back

Angle = \frac{1}{2}(arc1 + arc2), where arc1 and arc2 are the arcs intercepted by the angle.

Front

If two chords intersect inside a circle, how do you find the lengths of the segments?

Back

The products of the lengths of the segments of each chord are equal: a * b = c * d.

Front

What is the measure of an angle formed by a tangent and a secant?

Back

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