Angles in Circles Formed by Tangents, Secants and Chords

In a circle, a diameter bisects a chord and an arc with the same endpoints if and only if it is __________ to the chord.

• parallel

• congruent

• perpendicular

• bisect

If two chords intersect within a circle, then the measure of the angle formed is equal to half the ______ of the measures of the intercepted arcs.

• measures

• sum

• twice

• half

If a tangent and a secant, two secants, or two tangents intersect in a point in the exterior of a circle, then the measure of the angle formed is equal to one-half the ____________ of the measures of the intersected arcs.

• difference

• sum

• twice

• half

The measure of arc HJ = 110 degree and arc LJ = 150 degree, what is the measure of angle K?

Quadrilateral LOVE is inscribed in the circle as shown. If the measure of angle V = 140 degree, what is the measure of arc ELO?

• 140⁰

• 80⁰

• 280⁰

• 40⁰

What is the relationship between two tangents that share a common endpoint outside of the circle?

• One is half of the other.

• They are perpendicular.

• They are congruent.

• They are parallel.

What is the relationship between an angle formed by two chords and its intercepted arcs?

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

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

• The arc is half the angle.

• The arc is half the sum of the angles.

Determine the measure of ∠NOP

• 15°

• 20°

• 40°

• 50°

Find the measure of angle ABD.

• 14

• 51

• 37

• 65

What is the measure of angle 2?

• 80

• 45

• 125

• 40