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Section 10-4. Other Angle Relationships in Circles. Theorem 10-12. If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one half the measure of its intercepted arc. A. is tangent to Circle O. is a chord in Circle O. O. T. P. Example:.
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Section 10-4 Other Angle Relationships in Circles
Theorem 10-12 • If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one half the measure of its intercepted arc.
A is tangent to Circle O is a chord in Circle O O T P Example:
If two lines intersect a circle, there are three places where the lines can intersect.
Theorem 10-13 • If two chords intersect inside a circle, then the measure of each angle is one half the sum of the measures of the arcs intercepted by the angle and its vertical angle.
A D 1 C B
Theorem 10-14 • If a tangent and a secant, two tangents, or two secants, intersect outside a circle, then the measure of the angle formed is one half the difference of the measures of the intercepted arcs.
3 A tangent and a secant:
2 Two tangents:
1 Two secants: