Question

ements0Figure 2KLMIn circle J, KL = 14 and LM = 8. What is the circumference of thecircle? Round your answer to the nearest tenth, if necessary.Question 51 pts

Answer 1

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:

`\begin{gathered} KM^2=LM^2+KL^2 \\ KM^2=8^2+14^2 \\ KM^2=64+196 \\ KM^2=260 \\ KM=√(260) \\ KM\approx16.125 \end{gathered}`

Knowing the diameter of the circle, we can calculate the circumference as:

`\begin{gathered} C=\pi D \\ C=\pi *KM \\ C\approx3.1416*16.125 \\ C\approx50.7 \end{gathered}`

Answer: the circumference is 50.7 units long.