Embibe Experts Solutions for Exercise 1: West Bengal Board-2020

Prove that the tangent and the radius through the point of contact of a circle are perpendicular to each other.

If two circles touch each other externally then the point of contact will lie on the line segment joining the two centres -Prove it.

If a quadrilateral $ABCD$ is circumscribed about a circle with centre $O$, prove that $AB+CD=BC+DA$

The length of the radii of two circles are $8 \mathrm{cm}$ and $3 \mathrm{cm}$, the distance between the centres is $13 \mathrm{cm}$. What is the length of the direct common tangent of the two circles?

Prove that if two tangents are drawn to a circle from a point outside it, then they make equal angles at the centre.

The radius of a circle with centre $O$ is $5 cm$. $P$ is a point at a distance $13 cm$ from $O$. $PQ$ and $PR$ are two tangents to this circle. Find the area of the quadrilateral $PQOR$.