Question

Chords $AB$ and $CD$ of a circle when produced meet outside the circle at P. If $AB=4$cm, $BP=3$ cm and $CP=14$ cm, then the length of $CD$ is

• A. $3$ cm
• B. $4.5$ cm
• C. $6$ cm
• D. None of these

Answer 1

The correct option is D None of these

We know that if two secant segments are drawn to a circle from the same external point, the product of the length of one secant segment and its external part is equal to the product of the length of the other secant segment and its external part.

Here, two secants $AB$ and $CD$ meet outside the circle at P.

$AB=4$ cm; $BP=3$ cm and $CP=14$ cm

$PA\times PB=PC\times PD$

$\Rightarrow (4+3)\times 3=14\times PD$

$\Rightarrow P.D=1.5$ cm

$\Rightarrow CD=PC-PD=14-1.5=12.5$ cm