Big Ideas Math Geometry, 2014
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Big Ideas Math Geometry, 2014 View details
5. Angle Relationships in Circles
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Exercise 1 Page 566

Consider the Angles Inside the Circle Theorem (Theorem and the Angles Outside the Circle Theorem (Theorem

See solution.

Practice makes perfect
We have been given that points and are on a circle and intersects at point
With this information we will complete the following statement.
To fill in the blank we will recall the Angles Inside the Circle Theorem (Theorem and Angles Outside the Circle Theorem (Theorem

Angles Inside the Circle Theorem

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.

Angles Outside the Circle Theorem

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.

Since the measure of is one-half the difference of the measures of and by the Angles Outside the Circle Theorem we can conclude that point is outside the circle.
Therefore, we can complete the statement as follows.

If then point is outside the circle.