Bluebook SAT Test Circles 10

Question 1

A circle passes through the origin. Its center is at (5, 0). What is the equation of the circle?

Accepted Answer

(x−5)² + y² = 25

Answer

The radius = distance from (5,0) to (0,0) = 5. Equation: (x−5)² + y² = 25.

Question 2

In a circle, an inscribed angle measures 47°. Another inscribed angle intercepts the same arc. What is its measure?

Accepted Answer

47°

Answer

Inscribed angles that intercept the same arc are equal in measure.

Question 3

A circle has circumference C. What is the area of the circle in terms of C?

Accepted Answer

C²/(4π)

Answer

C = 2πr so r = C/(2π). Area = πr² = π(C/(2π))² = πC²/(4π²) = C²/(4π).

Question 4

The circle (x−2)² + (y+3)² = r² passes through the point (−1, 1). What is r²?

Accepted Answer

25

Answer

r² = (−1−2)² + (1−(−3))² = (−3)² + 4² = 9 + 16 = 25.

Question 5

Two circles have radii in the ratio 2:5. The area of the smaller circle is 12π. What is the area of the larger circle?

Accepted Answer

75π

Answer

Area ratio = (2:5)² = 4:25. If smaller area = 12π, larger = 12π × (25/4) = 75π.

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