Question

in the figure PA = 3cm AB= 9cm,PC = 4cm, find CD?​

Answer 1

Given:

PA = 3cm, AB= 9cm & PC = 4cm

To find:

The length of CD

Solution:

​To solve the given problem we will use the theorem of the Power of a point with respect to a circle which is as follows:

$\boxed{\bold{PA \times PB = PC \times PD\:...... where\:P\:is\: the\:point\:outside\:the \:circle }}$

From the figure, we have

PA = 3 cm

AB = 9 cm

PB = PA + AB = 3 + 9 = 12 cm

PC = 4 cm

PD = PC + CD

Now, on substituting the values in the theorem mentioned above, we get

$PA \times PB = PC \times PD$

$\implies PA \times (PA + AB) = PC \times (PC + CD)$

$\implies 3 \times 12 = 4 \times (4 + CD)$

$\implies 36 = 16 + 4CD$

$\implies 36 - 16 = 4CD$

$\implies 4CD = 20$

$\implies CD = \frac{20}{5}$

$\implies \bold{CD = 5 \:cm}$

Thus, the length of CD is → 5 cm.

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