Question

In the given figure, PQ is tangent to outer circle and PR is tangent to inner
circle. If PQ = 4cm, OQ = 3 cm and QR = 2 cm then find the length of PR.

Answer 1

hope it will help you.

Answer 2

Answer:

Length of PR is 4.58 cm.

Step-by-step explanation:

Given : PQ is tangent to outer circle and PR is tangent to inner circle. If PQ = 4cm, OQ = 3 cm and QR = 2 cm

To find: Length of PR

Solution : There are two concentric circles

OQ = 3 cm , PR=4 cm

PQ is tangent to outer circle and PR is tangent to inner circle i.e,

∠OQP = 90°

Applying Pythagoras theorem, In larger circle

$H^2=P^2+B^2$

$PO^2=PR^2+OQ^2$

$PO^2=4^2+3^2$

$PO^2=16+9$

$PO^2=25$

$PO=\sqrt{25}=5$

In ΔOPR,

RO= 2cm

PO = 5cm

PR=?

Now, Applying Pythagoras theorem

$H^2=P^2+B^2$

$PO^2=RO^2+PR^2$

$5^2=2^2+PR^2$

$25=4+PR^2$

$PR^2=21$

$PR=\sqrt{21}$

Therefore, Length of PR is 4.58 cm.