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SAT Topic 4

Circles

Circumference, area, arcs, sectors, and the equation of a circle.

Concept

For a circle of radius r:

Inscribed Angle Theorem: an inscribed angle equals half the central angle subtending the same arc.

Equation of a circle with center (h, k) and radius r:

(x − h)² + (y − k)² = r²

Worked example 1

A circle has radius 6. Find the arc length and sector area for a central angle of 60°.

Solution
Arc. L = (60 / 360) · 2π(6) = (1/6) · 12π = 2π
Sector. A = (60 / 360) · π(36) = (1/6) · 36π = 6π
Arc: 2π. Sector: 6π.

Worked example 2

Write the equation of the circle with center (3, −4) that passes through the point (6, 0).

Solution
Find r. Distance from (3, −4) to (6, 0): r = √(3² + 4²) = √25 = 5
Plug in. (x − 3)² + (y + 4)² = 5² = 25
(x − 3)² + (y + 4)² = 25.

Practice test

8 questions on circumference, area, arcs, sectors, and the standard circle equation.

Practice test · 8 questions Question 1 of 8 · Score 0