Embibe Experts Solutions for Chapter: Circles, Exercise 1: Exercise

The distance between the centres of two circles of radii $3 cm$ and $8 cm$ is $13 cm$. The points of contact of a direct common tangent to the circles are $P$ and $Q$. The length of $PQ$ is _____.

From an external point $A$, a tangent is drawn to a circle with centre $O$ and the tangent touches the circle at $B$. If $OB=9 \mathrm{cm}, AO=15 \mathrm{cm}$, then the length of $AB$ is

Two circles touch externally at $A$. A common tangent $PQ$ to two circles touches the circles at $P$ and $Q$. Then the measure of $\angle PAQ$ is

The rectangle circumscribed about a circle is a square. Prove it.

$AB$ and $AC$are two tangents to a circle from an external point $A$. $P$ is the point on the arc $BC$ and the tangent at $P$ intersects $AB$ and $AC$ at $D$ and $E$. Prove that the perimeter of $∆ADE$ is $2AB$

$AB$ is a chord of a circle with centre $O$ and $AP$ is a tangent. Prove that $\angle AOB=2\angle PAB$.

$PQ$ is a diameter of a circle and $A$ is a point on the circumference. $PR$ is perpendicular to the tangent at $A$. Prove that $PA$ bisects $\angle QPR$.

The tangents at $A$ and $B$ of a circle meet at $P$. If $\angle APB=56°$, then what is the value of $\angle PAB$?