Question

The diagram above shows a circle with centre O and radius 25 cm.

Given PR = 40 cm, MR = 21 cm and PR = KM, find the perimeter, in cm, of the pentagon OLMRQ.​

Answer 1

Explanation:

Notice that KL = LM and PQ = QR since OL and OQ are perpendicular to both KM and PR.

It follows that QR = (1/2) PR = 20 cm. We also know that MR = 21.

Now in order to solve the problem we just need OQ=OL

`OQ^2=OR^2-QR^2= 25^2-20^2 =225\\OQ=15`

Therefore the perimeter of the pentagon is

`OL+LM+MR+RQ+Q)\\= 15+20+21+20+15= 91`