Length of Internal Common Tangent

Q. Assertion : If in a circle, the radius of the circle is $3cm$ and distance of a point from the centre of a circle is $5cm$, then length of the tangent will be $4cm$.
Reason : $(\text{hypotenuse}{)}^2=(\text{base}{)}^2+(\text{height}{)}^2$

1. Both assertion (A) and reason (R) are true and reason $\left(R\right)$ is the correct explanation of assertion (A).
   
2. Assertion (A) is false but reason (R) is true.
3. Assertion (A) is true but reason (R) is false.
4. Both assertion (A) and reason (R) are true but reason $\left(R\right)$ is not the correct explanation of $\mathrm{assertion}\left(A\right)$.

Q.

If one circle lie completely outside the other circle, P, the intersection of transverse (indirect) common tangent, lie on the line joining the centers of the two circles and divide it internally in the ratio of their radii

1. True

2. False

Q. Three equal circles each of radius $r$ touch one another. The radius of the circle touching all the three given circles internally is

1. $\frac{(2+\sqrt{3})}{\sqrt{3}}r$
2. $(2+\sqrt{3})r$
3. $\frac{(2-\sqrt{3})}{\sqrt{3}}r$
4. $(2-\sqrt{3})r$

Q.

Length of internal (transverse) common tangent to two circles is $L_{int}=\sqrt{d^2-(r_1-r_2{)}^2}$

Where d = distance between the centers of the two circles $r_1\&r_2$ are radii of two circles

1. True

2. False