Bluebook SAT Test Circles 7

Question 1

A circle has area 25π. What is the circumference?

Accepted Answer

10π

Answer

πr²=25π → r=5; circumference=2π(5)=10π.

Question 2

Convert 210° to radians.

Accepted Answer

7π/6

Answer

210° × (π/180°) = 210π/180 = 7π/6.

Question 3

The circle x² + y² = 25 has center at the origin. Which of the following points lies inside the circle?

Accepted Answer

(3, 3)

Answer

3²+3²=18<25, so (3,3) is inside; all others satisfy x²+y² ≥ 25.

Question 4

A sector has central angle 3π/2 radians and area 27π/2. What is the radius?

Accepted Answer

3

Answer

A=½r²θ → 27π/2=½r²(3π/2)=(3πr²/4) → r²=9 → r=3.

Question 5

The central angle in a circle is 5 times the inscribed angle intercepting the same arc. What is the inscribed angle?

Accepted Answer

This cannot happen; a central angle is always exactly 2× the inscribed angle

Answer

By the Inscribed Angle Theorem, the central angle is always exactly twice the inscribed angle—it can never be 5 times it.

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