Embibe Experts Solutions for Chapter: Circles, Exercise 1: Nagaland Board-2020

In the adjoining figure, $PA$ and $PB$ are two tangents to the circle with centre $O$, such that $\angle AOB=110°$, then $\angle APB$ is

Two tangents$TP$ and $TQ$ are drawn to a circle with centre $O$ from an external point $T$. Prove that $\angle PTQ=2\angle OPQ$.

In the adjoining figure, $△ABC$ is right-angled at $B$. If $BC=6 \mathrm{cm}$ and $AB=8 \mathrm{cm}$, find the radius of the incircle. 

Two concentric circles have radii $10 \mathrm{cm}$ and $6 \mathrm{cm}$. The length of the chord of the larger circle which is a tangent to the smaller circle is

In the figure, $a, b, c$ are the sides of a right triangle where $c$ is the hypotenuse. Prove that the radius $r$ of the circle which touches the sides of the triangle is given by $r=\frac{a+b+c}{2}$.

In the adjoining figure, $PQ, RS$ and $XY$ are tangent at $A, B$ and $Z$ respectively. $AOB$ is the diameter of the circle. If $\angle AXO=25°$, find $\angle BOX$.

Prove that the parallelogram circumscribing a circle is a rhombus.

Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.