In the figure given below, diameter $A B$ and $C D$ 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 the length of tangent $P T$ (in $c m$ ).

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Solution

Since chord $C D$ and tangent at point $T$ intersect each other at $P$ ,
$∴ P C \times P D = P T^{2} . . . . . (1)$
$P T^{2} = (P D + C D) \times P D = 12.8 \times 5$
$\Rightarrow P T^{2} = 64$
$\Rightarrow P T = 8 c m =$ Length of tangent.

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Q. In the given figure, diameter

A B

and chord

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of a circle meet at

P . P T

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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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A B

ii. The length of tangent

P T

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$\frac{P A \times P B}{C D \times B D}$ =?

In the given figure PQ is a diameter of a circle with centre O and PT is a tangent at P. QT meets the circle at R. If ∠POR = $72^{\circ}$ , find $∠$ PTR.

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In the figure given below, diameter AB and 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 the length of tangent PT (in cm).

Since chord CD and tangent at point T intersect each other at P,∴PC×PD=PT2.....(1)PT2=(PD+CD)×PD=12.8×5⇒PT2=64⇒PT=8 cm= Length of tangent.

In the figure given below, diameter $A B$ and $C D$ 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 the length of tangent $P T$ (in $c m$ ).

Since chord $C D$ and tangent at point $T$ intersect each other at $P$ ,
$∴ P C \times P D = P T^{2} . . . . . (1)$
$P T^{2} = (P D + C D) \times P D = 12.8 \times 5$
$\Rightarrow P T^{2} = 64$
$\Rightarrow P T = 8 c m =$ Length of tangent.