This video tutorial covers three theorems related to tangents and secants in circles. Theorem 12.5.1 discusses the relationship between tangent-secant angles and their intercepted arcs. Theorem 12.5.2 explains how angles formed by intersecting chords or secants inside a circle are half the sum of their intercepted arcs. Theorem 12.5.3 focuses on angles formed by tangents and secants intersecting outside a circle, which are half the difference of their intercepted arcs. The video includes proofs and examples to illustrate these concepts.

What does Theorem 12.5.1 state about the angle formed by a tangent and a secant intersecting at the point of tangency?

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

• The angle is unrelated to the intercepted arc.

• The angle is twice the measure of the intercepted arc.

• The angle is half the measure of the intercepted arc.

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CCSS.HSG.C.A.2

According to Theorem 12.5.2, what is the measure of an angle formed by two secants intersecting inside a circle?

• Half the difference of the intercepted arcs.

• Half the sum of the intercepted arcs.

• Equal to the intercepted arcs.

• Twice the sum of the intercepted arcs.

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CCSS.HSG.C.A.2

In the proof of Theorem 12.5.2, what is the reason for drawing line BD?

• Because two points determine a line.

• To determine the length of the chord.

• To create a right angle.

• To bisect the angle.

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CCSS.HSG.C.A.2

When applying Theorem 12.5.2, what operation is used to find the angle measure when secants intersect inside the circle?

• Subtraction of intercepted arcs.

• Addition of intercepted arcs.

• Multiplication of intercepted arcs.

• Division of intercepted arcs.

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CCSS.HSG.C.A.2

What is the measure of angle SQR if arc PT is 32 degrees and arc SR is 100 degrees?

• 66 degrees

• 132 degrees

• 32 degrees

• 100 degrees

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CCSS.HSG.C.A.2

What does Theorem 12.5.3 state about the angle formed by a tangent and a secant intersecting outside a circle?

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

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

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

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

Tags

CCSS.HSG.C.A.2

According to Theorem 12.5.3, what operation is used to find the angle measure when intersections occur outside the circle?

• Addition of intercepted arcs.

• Subtraction of intercepted arcs.

• Multiplication of intercepted arcs.

• Division of intercepted arcs.

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CCSS.HSG.C.A.2

In the example of finding the value of x using Theorem 12.5.3, what is the first step if not all arc measures are given?

• Ignore the missing arc measure.

• Calculate the total circle measure and subtract the known arc.

• Use the given arc measures directly.

• Assume the missing arc is zero.

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CCSS.HSG.SRT.C.8

What should you check for when solving problems involving exterior intersections and missing arc measures?

• If the arcs are parallel.

• If the arcs form a complete circle.

• If the arcs are perpendicular.

• If the arcs are equal.

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CCSS.HSG.C.A.2

What is the measure of angle 1 if arc AD is 174 degrees and arc BD is 98 degrees?

• 38 degrees

• 136 degrees

• 98 degrees

• 76 degrees

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CCSS.HSG.C.A.2