Question

PR and PS are two tangents drawn from an external point P of the circle with centre at O , PR=8 cm and RS=60°, then the length of RS is :-

(a) 9cm
(b) 8cm
(c) 10cm
(d) 4cm​

Answer 1

option C will be the answer

Step-by-step explanation:

Given legth of PQ=8cm

length of OQ = 6cm

PQ is tangent 

therefore ∠OQP=90

so by apply pythoguras theorem 

we can find $OP$$$

OP2=OQ2+PQ2

OP2=62+82

OP=10cm

therfore,option C will be the answer

Answer 2

Given,

• PR and PS are two tangents drawn from an external point P of the circle.

• PR=8 cm and angle RPS=60°

To find,

The length of RS.

Solution,

Two tangents are drawn to the circle. The tangent forms a right-angled triangle connecting the line segment to the centre of the circle.

ΔPRO is a right-angled triangle.

Angle RPS is bisected by the line segment PO. Thus, angle RPO is 30°

In ΔPRO,

Tan30° = perpendicular/ base

          $\frac{1}{\sqrt{3} }$  = OR/RP

           $\frac{1}{\sqrt{3} } = \frac{OR}{8} \\\frac{8}{\sqrt{3} } = OR$

The length of OR or the radius of the circle is  $\frac{8}{\sqrt{3} }$.

In ΔRTO, where T is the point of intersection of RS and PO.

Length of RT = ORsin60°

                RT = $\frac{8}{\sqrt{3} }*\frac{\sqrt{3} }{2} = 4$

RS length is equal to the sum of RT and TS.

Therefore, the complete length of RS = 2*4 = 8cm.