15
QuizMultiple Choice

Area of a Circle and a Sector — Unit test

Question 15 • *CR CCSS Math 2 S2 [M2960OX]

Triangle JKL is equilateral. One side of the triangle, JL, is a diameter of circle M. Which is true about line segments JK and KL?

Answer
A
Both segments are tangent to circle M but are not chords.
B
One segment is tangent to circle M and one segment is a chord in circle M.
C
Both segments are chords in circle M but are not tangents.
D
Neither segment is a chord nor tangent to circle M.

Explanation

Because JL is a diameter, the circle’s radius is half the length of JL. In an equilateral triangle, K lies a distance of √3/2 times JL from the midpoint of JL, which is greater than the circle’s radius, so K is outside the circle. Thus JK and KL each have one endpoint on the circle and one outside; neither is a chord, and neither is tangent because each meets the circle at an endpoint while passing into the circle’s interior.

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