Question

hey friends... answer this question...

Answer 1

hey mate
here's the solution....

Answer 2

Answer:

Length of PR is 19 cm.

B is correct option.

Explanation:

PQ is diameter of larger circle.

Radius OQ is half of PQ

Radius of larger circle OQ= 13 cm

Radius of smaller circle OR = 8 cm

QR is tangent on inner circle at point R.

OR is perpendicular to QR because radius perpendicular to tangent.

In ΔORQ, ∠ORQ=90°

Using pythagoreous theorem,

$QR^2=OQ^2-OR^2$

$QR=\sqrt{13^2-8^2}\Rightarrow \sqrt{105}$

$\cos (\angle OQR)=\frac{\sqrt{105}}{13}$

In ΔPRQ, Using cosine law

$a^2=b^2+c^2-2bc\cos A$

$\therefore PR^2=PQ^2+RQ^2-2\times PQ\times RQ \times \cos (\angle PQR)$

$\text{where, } PQ=26 , RQ=\sqrt{105} , \cos (\angle OQR)=\frac{\sqrt{105}}{13}$

Substitute into above formula and solve for PR

$PR^2=26^2+(\sqrt{105})^2-2\times 26\times \sqrt{105}\times \frac{\sqrt{105}}{13}$

$PR^2=676+105-420\Rightarrow 361$

$PQ=\sqrt{361}\Rightarrow 19\text{ cm}$

Thus, Length of PR is 19 cm.

B is correct option.