Bluebook SAT Test Circles 4

Question 1

What is the center of the circle x² + y² − 10x + 4y + 20 = 0?

Accepted Answer

(5, −2)

Answer

Complete the square: (x−5)²+(y+2)² = 25+4−20 = 9; center (5,−2).

Question 2

A central angle of π/6 radians corresponds to how many degrees?

Accepted Answer

30°

Answer

(π/6)(180°/π) = 180°/6 = 30°.

Question 3

A circle has diameter 14. What is its area?

Accepted Answer

49π

Answer

r = 14/2 = 7; area = π(7)² = 49π.

Question 4

An arc subtends a central angle of 5π/6 radians in a circle of radius 6. What is the arc length?

Accepted Answer

5π

Answer

s = rθ = 6·(5π/6) = 5π.

Question 5

Two inscribed angles in the same circle intercept the same arc. What is the relationship between the two angles?

Accepted Answer

They are equal

Answer

Inscribed angles that intercept the same arc are equal (both equal half the arc measure).

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