Prove that angles inscribed in the semi circle are right angle.

In the figure, $\mathrm{O}$ is the centre of a circle, $\mathrm{AC}$ is a diameter. If $\angle \mathrm{ACB} = 50°$, then find the measure of $\angle \mathrm{BAC}$(in $°$).

In the figure given below, $O$ is the centre of the circle and $AB$ is a diameter. If $AC=BD$ and $\angle AOC=72°$. Find $\angle BAD$.

The angle subtended by the diameter of a circle at a point on the circumference is _____.

$AB$ is the diameter of the circle. $D$ is the point on the circle.

$\angle ACB+\angle ADB+\angle AEB=270°$. The measure of one among $\angle ACB, \angle ADB$ and $\angle AEB$ is $110°$ . Write the measures of $\angle ACB, \angle ADB, \angle AEB$.

In the figure given below $O$ is the centre of the circle. If the $QR=OP$ and angle $\angle ORP=20°$. Find the value of $x$ giving reasons.

In the given figure $O$ is the centre of the circle, $\angle AOC=80°$

What is the measure of $\angle ABC$

In the figure given below, $O$ is the centre of the circle and $AB$ is a diameter. If $AC=BD$ and $\angle AOC=72°$. Find $\angle ABC$.

Prove that the angle formed by an arc on the centre of the circle is twice the angle formed at any point of remaining part of the circle.

In the given figure, $ABCDE$ is a pentagon inscribed in a circle such that $AC$ is a diameter and side $BC\parallel AE$. If $\angle BAC=50°$, find giving reason

$\angle BEC$

In the figure given below, $O$ is the centre of the circle and $AB$ is a diameter. If $AC=BD$ and $\angle AOC=72°$. Find $\angle ABD$ in degrees.

A sector of radius $12 centimetres$ and central angle $120°$ is rolled up into a cone. What is the central angle of the sector to be used to make a cone of base radius $\sqrt{2} centimetres$ and height $4 centimetres$?

In the figure, the chord $\mathrm{BD}$ is perpendicular to the diameter $\mathrm{AC}$. Find the measure of $\angle CDM$. (in $°$).

Prove that, the angles in the same segment of a circle are equal to each other.

In the given figure $O$ is centre of a circle, $\angle AOB = 40°$ and $\angle BDC = 100°$ then the value of $\angle OBC$ will be

In the given figure a quadrilateral $ABCD$ have $AB=AC=AD$, then prove that $\angle BAD=2(\angle BDC+\angle CBD)$.

In the given figure, $ABCDE$ is a pentagon inscribed in a circle such that $AC$ is a diameter and side $BC\parallel AE$. If $\angle BAC=50°$, find giving reason $\angle EDC$.

In the given figure $TP$ and $TQ$ are two tangents to the circle with centre $O$, touching at $A$ and $C$ respectively. If $\angle BCQ=55°$ and $\angle BAP=60°$, find$\angle AOC.$