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Standard XII

Mathematics

Length of Internal Common Tangent

In the given ...

Question

In the given figure, diameter $A B$ and chord $C D$ of a circle meet at $P . P T$ is a tangent to the circle at $T . C D = 7.8 c m$ , $P D = 5 c m, P B = 4 c m$ . Find:
i. $A B$
ii. The length of tangent $P T$ .

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Solution

$\begin{matrix} g i v e n C D = 7.8 c m P D = 5 c m P B = 4 c m I n g i v e n f i g u r e - (1) P B \times P A = P D \times P C 4 \times P A = 5 \times 12.8 P A = 16 c m (A B = 12 c m) (2) (C D + P D) \times P D = P T^{2} (7.8 + 5) \times 5 = P T^{2} 64 = P T^{2} P T = 8 c m \end{matrix}$

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Similar questions

Q. In the figure given below, diameter

A B

and

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T . C D = 7.8 c m, P D = 5 c m . P B = 4 c m

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In the figure given below, diameter AB and chord CD of a circle meet at P. PT is a tangent to the circle at T. CD=7.8 cm, PD = 5 cm, PB = 4 cm. Select the statements that are true.

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In the given figure, diameter AB and chord CD of a circle meet at P.PT is a tangent to the circle at T.CD=7.8 cm , PD=5 cm,PB=4 cm. Find:i. ABii. The length of tangent PT.

givenCD=7.8cmPD=5cmPB=4cmIngivenfigure−(1)PB×PA=PD×PC4×PA=5×12.8PA=16cm(AB=12cm)(2)(CD+PD)×PD=PT2(7.8+5)×5=PT264=PT2PT=8cm

In the given figure, diameter $A B$ and chord $C D$ of a circle meet at $P . P T$ is a tangent to the circle at $T . C D = 7.8 c m$ , $P D = 5 c m, P B = 4 c m$ . Find:
i. $A B$
ii. The length of tangent $P T$ .

$\begin{matrix} g i v e n C D = 7.8 c m P D = 5 c m P B = 4 c m I n g i v e n f i g u r e - (1) P B \times P A = P D \times P C 4 \times P A = 5 \times 12.8 P A = 16 c m (A B = 12 c m) (2) (C D + P D) \times P D = P T^{2} (7.8 + 5) \times 5 = P T^{2} 64 = P T^{2} P T = 8 c m \end{matrix}$