Question

Two concentric circle with centre O are of radii 6 cm and 3 cm. From an external
point P, tangents PA and PB are drawn to these circle as shown in the figure. If
AP = 10 cm. Find BP

Answer 1

Hope it will help uh mine friend !!

Answer 2

Answer:

Length of BP is 11.2 cm.

Step-by-step explanation:

Given : Two concentric circle with center O are of radii 6 cm and 3 cm. From an external  point P, tangents PA and PB are drawn to these circle as shown in the figure. If  AP = 10 cm.

To find: Length of BP

Solution : There are two concentric circles

AO = 6 cm (larger circle)

BO = 3 cm (smaller circle)

PA and PB are tangents on the circle i.e, ∠OAP = ∠OBP = 90°

Applying Pythagoras theorem, In larger circle

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

$OP^2=AO^2+AP^2$

$OP^2=6^2+10^2$

$OP^2=36+100$

$OP^2=136$

$OP=\sqrt{136}$

Now, Applying Pythagoras theorem, In smaller circle

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

$OP^2=BO^2+BP^2$

$\sqrt{136}^2=3^2+BP^2$

$136=9+BP^2$

$BP^2=127$

$BP=\sqrt{127}$

$BP=11.2$

Therefore, Length of BP is 11.2 cm.