Bluebook SAT Test Circles 6

Question 1

Write the equation of a circle with center (7, −3) and radius 4.

Accepted Answer

(x − 7)² + (y + 3)² = 16

Answer

Standard form: (x−7)²+(y−(−3))²=4² → (x−7)²+(y+3)²=16.

Question 2

A circle has a central angle of 240° and a radius of 3. What is the arc length?

Accepted Answer

4π

Answer

Arc = (240/360)(2π·3) = (2/3)(6π) = 4π.

Question 3

An inscribed angle of 65° intercepts an arc. The central angle subtending the same arc is:

Accepted Answer

130°

Answer

Central angle = 2 × inscribed angle = 2 × 65° = 130°.

Question 4

The diameter of a circle is the chord passing through the center. If an inscribed angle intercepts the diameter, what is the angle's measure?

Accepted Answer

90°

Answer

The diameter subtends a semicircle (180°), and an inscribed angle is half the arc = 90° (Thales' theorem).

Question 5

Rewrite x² + y² + 12x − 16y + 75 = 0 in standard form. What is the radius?

Accepted Answer

5

Answer

(x+6)²+(y−8)²=36+64−75=25; radius=√25=5.

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