SAT Math Multiple Choice Practice Question 457: Answer and Explanation

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Question: 457

19. Point K lies outside the circle with center C such that CK = 26. is tangent to the circle at point J, and the distance from J to K is 2 less than the distance from K to C. What is the circumference of the circle?

A. 10π
B. 15π
C. 20π
D. 22π
E. 24π

Correct Answer: C


C Draw a picture! Look at triangle CJK. ∠CJK is 90° because the radius of a circle is always perpendicular to a line tangent to that circle. Use the Pythagorean theorem, (CJ)2 + 242 = 262, or your knowledge of right triangles (this is a multiple of a 5:12:13 triangle) to get CJ = 10, which represents the radius of the circle. So the circumference of the circle = 2π × 10 or 20π.

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