Geometry Question

Question

In the diagram, triangle MOK is inscribed in Circle C in such that segment MK is a diameter of the circle, and angle OMK is congruent to angle OKM.

If OK=3 feet, what is the length of the diameter, segment MK?

6 feet

6 sqrt2 feet

3 sqrt2 feet

3 sqrt3 feet

Answer 1

Given that MK is the diameter of circle C, ΔOMK is a right triangle with ∠MOK = 90º (regardless of where O is, since ∠MOK is an inscribed angle)

Now, because you also know that ∠OMK ≅ ∠OKM = 45º, ΔOMK is a 45º - 45º - 90º traingle. So, if OK = 3 = OM, then MK = 3√2, which is the length of the diameter of circle C.

Hope this helps

Mr. K

Answer 2

Put M and K at the extreme left and right sides of the circle

Put O at the top of the circle. Let C be the center of the circle.

OCM and OCK are right angles, with 45 degrees for the other 2 angles

Angles OMK and OKM are both 45 degrees.

That makes OC the radius = 3, and MK is the diameter = twice the radius or 2x3 = 6 feet