Question

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?

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

Answer 1

Neither segment is a chord nor a tangent.

Reason: JL is the diameter, so its midpoint is the circle's center and the radius is JL/2. In the equilateral triangle the distance from that midpoint to K (the triangle's height) is (sqrt(3)/2)·JL, which is larger than JL/2, so K is outside the circle. JK and KL therefore have only one endpoint on the circle (J or L) and are not perpendicular to the radius at that point, so they are neither chords (both endpoints on the circle) nor tangents (touching at exactly one point with perpendicular radius).