Question

the radii of two concentric circles are 13 cm and 8 cm. AB is the diameter of the bigger circle and BD is a tangent to the smaller circle touching it at D and intersects on the larger circle at P on producing. find the length of AP

Answer 1

answer is 16cm
I hope this will help you...

Answer 2

Answer:

AP =16 cm

Step-by-step explanation:

Given: Concentric circles with centro O with radii 13 cm and 8 cm

To find: lenght of AP

In figure BP is chord for bigger circle.

BD is tangent to smaller circle

∠ODB = 90° (because radius and tangent are perpendicular to each other

                       at point of contact )

⇒ chord BP is perpendicular to OD

⇒ BD = DP ( because perpendicular from center bisect the chord).......... 1

In ΔBOD

By Pythagoras theorem,

$BO^2 = BD^2+OD^2$

$13^2 = BD^2+8^2$ (since, BO and OD are radii)

$169= BD^2+64$

$BD^2=169-64$

$BD^2=105$

$BD=\sqrt{105}$

from eqn 1,

BP = 2 × BD

BP = 2$\sqrt{105}$ cm

In ΔABP

∠APB = 90° ( because angle made by diameter in semicircle is right angle)

By Pythagoras theorem,

$AB^2 = BP^2+AP^2$

$26^2 = (2\sqrt{105})^2+AP^2$

$676 = 4×105 +AP^2$

$AP^2 = 676 -420$

$AP^2 = 256$

$AP=\sqrt{256}$

$AP=16$

Therefore, AP =16 cm