List of top Mathematics Questions on Circles asked in UP Board X

A chord of a circle of radius 14 cm subtends an angle of 60° at the centre. Find the areas of the corresponding minor and major segments of the circle.

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A solid is in the shape of a cone standing on a right circular cylinder with both their radii being equal to 7.5 cm and the height of the cone is equal to its radius. If the total height of the solid is 22.5 cm, find the volume of the solid. (Use $\pi = 3.14$, $\sqrt{3} = 1.732$)
The two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that $\angle PTQ = 2 \angle OPQ$.
If an arc of a circle of radius 10.5 cm, subtends an angle of 60° at the centre, then find the length of the arc.
The angle of a sector of a circle with radius 4 cm is 30°. The area of the sector will be :
Prove that the lengths of tangents drawn from an external point to a circle are equal.
The tangent PQ of a circle of radius 5 cm meets at a point Q on the line passing through the centre O. If OQ = 12 cm, then the measure of PQ will be
An arc of a circle of radius 6 cm subtends an angle of $30^\circ$ at the centre. The measure of the corresponding arc will be
Prove that the lengths of tangents drawn from an external point to a circle are equal.
The length of tangent from a point Q to a circle is 24 cm and the distance of Q from the centre of circle is 25 cm. Then radius of the circle will be
If tangents PA and PB from a point P to a circle with centre O are inclined to each other at an angle of 80°, then $\angle POA$ will be
Area of the sector of an angle $\theta^\circ$ of a circle with radius $r$ will be
Prove that the angle between the tangents drawn from an external point to a circle is supplementary to the angle formed by the line segment joining the points of contact at the centre of the circle.
Number of parallel tangent lines drawn to the end points of the diameter of a circle will be
The area of the sector of a circle whose angle is \(60^\circ\) and radius \(12 \, \text{cm}\) will be
If the area of a sector of a circle of radius 14 cm is 154 cm\(^2\), then the angle of the sector will be:
Prove that in two concentric circles, the chord of the larger circle which touches the smaller circle is bisected at the point of contact.
The area of a quadrant of a circle whose circumference is 22 cm will be:
The length of a tangent from a point A at a distance 7.5 cm from the centre of the circle is 6 cm. Find the radius of the circle.