Inscribed Angles Mastery
Grade 12 Geometry worksheet focusing on inscribed angles, their properties, and related theorems.
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Inscribed Angles Mastery
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Read each question carefully and provide your answers in the space provided. Show all your work for full credit.
1. An inscribed angle is formed by two chords in a circle that share a common endpoint. What is the relationship between the measure of an inscribed angle and the measure of its intercepted arc?
The inscribed angle is equal to the intercepted arc.
The inscribed angle is half the measure of the intercepted arc.
The inscribed angle is twice the measure of the intercepted arc.
There is no direct relationship between them.
2. If an inscribed angle intercepts a semicircle, what is the measure of the inscribed angle?
45 degrees
90 degrees
180 degrees
Depends on the radius of the circle
3. In the circle below, if the measure of arc AB is 80 degrees, what is the measure of inscribed angle ACB?
Work:
4. Given a cyclic quadrilateral ABCD, where angle A = 100 degrees and angle B = 85 degrees. Find the measures of angles C and D.
Work:
5. Angles inscribed in the same arc are .
6. The opposite angles of a cyclic quadrilateral are .
7. A central angle that intercepts the same arc as an inscribed angle is twice the measure of the inscribed angle.
True
False
8. If a quadrilateral is inscribed in a circle, then its opposite angles are complementary.
True
False
9. A circle has a chord of length 10 cm. An inscribed angle subtending this chord measures 60 degrees. What is the radius of the circle?