Question

In the figure, the chord AB and CD of the circle intersect internally
at a point P, If AP = 4 cm, PB = 3 cm and CP = 2 cm then the
measure of DP will be :

​

Answer 1

Step-by-step explanation:

$\color{darkblue} \begin{aligned} \text { Given - } \tt A P & \tt=4 cm \\ \\ \tt P B & \tt=3 cm \\ \\\tt C P & \tt=2 cm \end{aligned}$

To Find - D P=?

$\color{darkcyan} \underline{ \begin{array}{ || |l| || } \hline \color{magenta} \\ \hline \boxed{ \text{ \tt \: Solution:-} } \end{array}}$

$\pmb{ \color{darkgreen}\[ \begin{aligned} \tt A P \times P B & \tt=C P \times D P \\ \\ \tt 4 \times 3 & \tt=2 \times D P \\ \\ \tt 12 & \tt=2 \times D P \\ \\ \tt D P & \tt=\frac{12}{2} \\ \\ \tt \therefore \qquad \boxed{ \tt D P }& \boxed{ \tt=6 cm .}\end{aligned} \]}$