List of top Mathematics Questions on Geometry

A car is moving away from the base of a 30 m high tower. The angle of elevation of the top of the tower from the car at an instant, when the car is $10\sqrt{3}$ m away from the base of the tower, is :

If TP and TQ are two tangents to a circle with centre O from an external point T so that $\angle POQ = 120^\circ$, then $\angle PTQ$ is equal to :

In the given figure, PA is a tangent from an external point P to a circle with centre O. If $\angle POB = 125^\circ$, then $\angle APO$ is equal to :

The length of the arc of the sector of a circle with radius 21 cm and of central angle 60°, is :

The hour hand of a clock is 7 cm long. The angle swept by it between 7:00 a.m. and 8:10 a.m. is :

The total surface area of a solid hemisphere of diameter ‘2d’ is :

A solid is in the form of a cylinder with hemispherical ends. The total height of the solid is 20 cm and the diameter of the cylinder is 7 cm. Find the total volume of the solid. (Use $\pi = \frac{22}{7}$)

A brooch is crafted from silver wire in the shape of a circle with a diameter of 35 mm. The wire is also used to create 5 diameters, dividing the circle into 10 equal sectors.

(i) What is the radius of circle?
(ii) What is the circumference of the brooch?
(iii) (a) What is the total length of silver wire required? OR
(iii) (b) What is the area of each sector of the brooch?}

In the adjoining figure, if $EA \parallel SR$ and $PE = x$ cm, then the value of $5x$ is :

In the adjoining figure, the angle of elevation of the point C from the point B, is :

In the adjoining figure, the slant height of the conical part is :

Prove that the lengths of tangents drawn from an external point to a circle are equal.

In the adjoining figure, AB is the diameter of the circle with centre O. Two tangents p and q are drawn to the circle at points A and B respectively. Prove that p $\parallel$ q. Further, a line CD touches the circle at E and $\angle BCD = 110^\circ$. Find the measure of $\angle ADC$.

In the adjoining figure, $\triangle OAB$ is an equilateral triangle and the area of the shaded region is $750\pi$ cm$^2$. Find the perimeter of the shaded region.

Find the ratio of area of shaded region in figure (i) to that of figure (ii).

Mishika and Sahaj created a bird-bath from a cylindrical log of wood by scooping out a hemispherical depression. Cylinder length is 2 m (0.6 m in earth) and diameter is 1.4 m.
(i) Radius of depression?
(ii) Volume of water in hemisphere in terms of $\pi$?
(iii) (a) Total surface area of log above ground? OR
(iii) (b) Volume of log above ground?

In the adjoining figure, $\triangle CAB$ is a right triangle, right angled at A and $AD \perp BC$. Prove that $\triangle ADB \sim \triangle CDA$. Further, if $BC = 10$ cm and $CD = 2$ cm, find the length of AD.

In $\triangle ABC, DE || BC$. If AE = (2x + 1) cm, EC = 4 cm, AD = (x + 1) cm and DB = 3 cm, then value of x is

In the given figure, PA is tangent to a circle with centre O. If $\angle APO = 30^\circ$ and OA = 2.5 cm, then OP is equal to

In $\triangle ABC$, $DE \parallel BC$. If $AE = (2x+1)$ cm, $EC = 4$ cm, $AD = (x+1)$ cm and $DB = 3$ cm, then the value of $x$ is

In two concentric circles centred at O, a chord AB of the larger circle touches the smaller circle at C. If OA = 3.5 cm, OC = 2.1 cm, then AB is equal to

For a circle with centre O and radius 5 cm, which of the following statements is true?
P: Distance between every pair of parallel tangents is 10 cm.
Q: Distance between every pair of parallel tangents must be between 5 cm and 10 cm.
R: Distance between every pair of parallel tangents is 5 cm.
S: There does not exist a point outside the circle from where length of tangent is 5 cm.

In the adjoining figure, PA and PB are tangents to a circle with centre O such that $\angle P = 90^\circ$. If $AB = 3\sqrt{2}$ cm, then the diameter of the circle is

In the adjoining figure, TS is a tangent to a circle with centre O. The value of $2x^\circ$ is

In $\triangle ABC, \angle B = 90^\circ$. If $ \frac{AB}{AC} = \frac{1}{2} $, then cos C is equal to