Arc and Angle Measure Created by Intersecting Chords Secants and Tangents

Using the chord-chord theorem, if two chords intersect at point P, how do you express the relationship between the segments?

• AP * PB = CP * PD

• AP - PB = CP - PD

• AP * CP = PB * PD

• AP + PB = CP + PD

What is the secant-secant theorem and how is it applied in circle geometry?

• It states that the sum of the angles in a triangle is equal to 180 degrees.

• The secant-secant theorem calculates the area of a circle.

• The secant-secant theorem relates the lengths of two secants intersecting outside a circle, allowing calculation of unknown segment lengths.

• The theorem applies only to tangent lines touching the circle.

How does the measure of an inscribed angle compare to the measure of the central angle that subtends the same arc?

• The inscribed angle is half the measure of the central angle.

• The inscribed angle has no relation to the central angle.

• The inscribed angle is equal to the central angle.

• The inscribed angle is twice the measure of the central angle.

If the lengths of two intersecting chords are 6 and 8, what is the product of the segments created by their intersection?

• 36

• 48

• 24

• 56

What is the relationship between the angles formed by two secants that intersect outside the circle?

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

• The angle is equal to the difference of the intercepted arcs.

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

• The angle is equal to the sum of the intercepted arcs.

If an inscribed angle measures 30 degrees, what is the measure of the intercepted arc?

• 30 degrees

• 90 degrees

• 120 degrees

• 60 degrees

How can you prove that the angle formed by a tangent and a chord through the point of contact is equal to the inscribed angle on the opposite arc?

• The angle formed by a tangent and a chord is always 90 degrees.

• The angle formed by a tangent and a chord is equal to the angle formed by two tangents.

• The angle formed by a tangent and a chord through the point of contact is equal to the inscribed angle on the opposite arc.

• The angle formed by a tangent and a chord is equal to the angle formed by the secant and the chord.

What is the significance of the chord-chord theorem in solving problems related to circle geometry?

• The chord-chord theorem helps in finding lengths of segments formed by intersecting chords in a circle.

• The chord-chord theorem applies only to triangles, not circles.

• The chord-chord theorem is used to calculate the circumference of a circle.

• The chord-chord theorem determines the area of a circle.