Perpendicular from right angle to hypotenuse divides the triangle into two similar triangles

Q. In given figure, if $\angle A=\angle C$, AB = 6cm, BP = 15cm, AP = 12cm and CP = 4cm, then find the lengths of PD and CD.

Q.

In the given figure, the ratio $\angle \mathrm{ABD}:\angle \mathrm{ACD}$ is

1. $1:1$

2. $2:1$

3. $1:2$

4. $2:3$

Q.

In a right $△$ABC, a perpendicular BD is drawn on to the largest side from the opposite vertex. Which of the following does not give the ratio of the areas of $△$ABD and $△$ACB?

1. $({\frac{AB}{AC})}^2$

2. $({\frac{AD}{AB})}^2$

3. $({\frac{BD}{CB})}^2$

4. $({\frac{AB}{AD})}^2$