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.

Question

asked Sep 12, 2022 159k views

1 Answer

Malcolmpdx · Answer 1 · 2022-09-16T23:31:02+0000

Answer:

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

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