Bluebook SAT Test Circles 3

Question 1

The equation (x − 1)² + (y + 7)² = 25 represents a circle. What are the center and radius?

Accepted Answer

Center (1, −7), radius 5

Answer

Standard form (x−h)²+(y−k)²=r²: h=1, k=−7, r=√25=5.

Question 2

A circle has area 100π. What is the diameter?

Accepted Answer

20

Answer

A = πr² = 100π → r² = 100 → r = 10 → diameter = 20.

Question 3

An arc length of 6π is cut from a circle of radius 9. What is the central angle in radians?

Accepted Answer

2π/3

Answer

Arc = rθ → 6π = 9θ → θ = 6π/9 = 2π/3.

Question 4

What is the area of a sector with radius 5 and central angle π/2 radians?

Accepted Answer

25π/4

Answer

Sector area = (1/2)r²θ = (1/2)(25)(π/2) = 25π/4.

Question 5

An inscribed angle intercepts a semicircle (arc of 180°). What is the measure of the inscribed angle?

Accepted Answer

90°

Answer

An inscribed angle is half the intercepted arc: 180°/2 = 90° (Thales' theorem).

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