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In the Given Figure, Oq : Pq = 3.4 and Perimeter of δ Poq = 60 Cm. Determine Pq, Qr and Op. - Mathematics

Short Note

In the given figure, OQ : PQ = 3.4 and perimeter of Δ POQ = 60 cm. Determine PQ, QR and OP.

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In the figure,

∠ PQD. Therefore we can use Pythagoras theorem to find the side PO.

`PO^2=PQ^2+OQ^2` …… (1)

In the problem it is given that,


`OQ= 3/4PQ`.....(2)

Substituting this in equation (1), we have,





It is given that the perimeter of  Δ POQis 60 cm. Therefore,

PQ + OQ + PO = 60

Substituting (2) and (3) in the above equation, we have,





Substituting for PQ in equation (2), we have,




OQ is the radius of the circle and QR is the diameter. Therefore,

QR = 2OQ

QR = 30

Substituting for PQ in equation (3), we have,



Thus we have found that PQ = 20 cm, QR = 30 cm and PO = 25 cm.

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RD Sharma Class 10 Maths
Chapter 8 Circles
Exercise 8.2 | Q 44 | Page 40
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