We have some points on the circumference (K, L and M).
As KM is a diameter of the circle, the angle ∠KLM will be a right angle for any location of L.
Then, if ∠KLM is a right angle, then KLM is a rith triangle.
Knowing KL = 14 and LM = 8, we can use the Pythagorean theorem to find KM:
[tex]\begin{gathered} KM^2=LM^2+KL^2 \\ KM^2=8^2+14^2 \\ KM^2=64+196 \\ KM^2=260 \\ KM=\sqrt{260} \\ KM\approx16.125 \end{gathered}[/tex]
Knowing the diameter of the circle, we can calculate the circumference as:
[tex]\begin{gathered} C=\pi D \\ C=\pi *KM \\ C\approx3.1416*16.125 \\ C\approx50.7 \end{gathered}[/tex]
Answer: the circumference is 50.7 units long.
