3.16 Unit Test: Circles - Part 1

This figure shows circle O with diameter QS. mRSQ=290° What is the measure of ∠ROQ? Enter your answer in the box. _________°

70°

Which explanation justifies how the area of a sector of a circle is derived? 1. Calculate the area of the circle. Then, determine the central angle of the sector and divide this angle by 360° to get a fraction. Multiply ​the area of the circle​ by this fraction. 2. Determine how many triangles can fit into a circle. Divide 360° by the number of triangles. Multiply the quotient by ​the area of the circle​ . 3. Partition the circle into unit squares. Determine the area of the sector and multiply the area by the degree of the circle. 4. Determine the degree of the sector. Divide by 180° and then multiply it by the area of the triangle the sector is in.

1. Calculate the area of the circle. Then, determine the central angle of the sector and divide this angle by 360° to get a fraction. Multiply ​the area of the circle​ by this fraction.

What is the length of ST¯¯¯¯¯? Enter your answer as a decimal in the box. Round your final answer to the nearest hundredth. _________in.

14.49 in.

This figure shows circle O with chords AC and BD . ​ mAB=34° mCD=34° AP=6 m ​PC=8 m What is BD ? Enter your answer in the box. ________m

14m

This figure shows circle O with inscribed ∠XYZ. m∠XYZ=76∘ What is the measure of XYZ? Enter your answer in the box. ______°

208°

In the figure, TR−→− and TV−→− are secants to circle A. mRV=99° mSU=45° What is the measure of ∠RTV? Enter your answer in the box. ______°

27°

AC←→ is tangent to the circle with center at B. The measure of ∠ACB is 58°. What is the measure of ∠ABC ? Enter your answer in the box. m∠ABC = _______°

32°

A circle has a radius of 4 ft. What is the area of the sector formed by a central angle measuring 3π/2 radians? Use 3.14 for pi. Enter your answer as a decimal in the box. _______ft²

37.68ft²

A circle has a radius of 6 in. What is the exact length of an arc formed by a central angle measuring 45°? Enter your answer in the box. Express your answer using π . ________in.

3π/2 in.

Quadrilateral ABCD ​ is inscribed in circle O. What is ​ m∠A ​ ? Enter your answer in the box. ________°

42°

Chord AC intersects chord BD at point P in circle Z. AP=3.5 in. DP=4 in. PC=6 in. What is BP? Enter your answer as a decimal in the box. ________in.

5.25 in.

Given: ​Quadrilateral ABCD​ is inscribed in circle O. Prove: m∠A+m∠C=180° Drag an expression or phrase to each box to complete the proof. Statements: Reasons​: 1. Quadrilateral ABCD​ is inscribed in circle O. Given 2. mBCD=2(m∠A) ? 3. ? ​ Inscribed Angle Theorem 4. TheoremmBCD+mDAB=360° ? 5. 2(m∠A)+2(m∠C)=360° Substitution Property​​ 6. ​ ? Division Property of Equality Options for ?: 7. Inscribed Angle Theorem 8. mBCD=2(m∠C) 9. The sum of arcs that make a circle are 360° 10. m∠A + m∠C = 180°

Statements: Reasons​: 1. Quadrilateral ABCD​ is inscribed in circle O. Given 2. mBCD=2(m∠A) 7. 3. 8. ​ Inscribed Angle Theorem 4. TheoremmBCD+mDAB=360° 9. 5. 2(m∠A)+2(m∠C)=360° Substitution Property​​ 6. ​ 10. Division Property of Equality