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

In the given figure, if $AB = AC$, then prove that $BE = EC$.

In the figure, $ \triangle ODC \sim \triangle OBA $. If $ \angle BOC = 125^\circ $ and $ \angle CDO = 70^\circ $, then the value of $ \angle OAB $ will be:

If a line intersects the sides AB and AC at D and E respectively in a triangle ABC and it is parallel to the side BC, then prove that \[ \frac{AD}{AB} = \frac{AE}{AC} \]

In the figure, $ OA, OB, OC, OD $ are drawn such that $ OB = OC $ and $ OA = OD $. Show that $ \angle A = \angle C $ and $ \angle B = \angle D $.

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

A tangent PQ at a point P of a circle of radius 10 cm meets a line through the centre O at a point Q so that OQ = 12 cm. The length of PQ will be:

If $ BL $ and $ CM $ are medians of a right triangle $ ABC $ whose $ \angle A = 90^\circ $, then prove that: $ 4(BL^2 + CM^2) = 6 BC^2 $.

In the figure $ OA \cdot OB = OC \cdot OD $, then prove that $ \angle A = \angle C $ and $ \angle B = \angle D $.

If ratio of sides of two similar triangles is 4:7, then ratio of their areas will be:

If the length of diagonals of a rhombus are 12 cm and 16 cm, then the length of the side of the rhombus will be:

Construct $ \triangle ABC $ in which $ BC = 6 \, \text{cm} $, $ AB = 3 \, \text{cm} $, and $ \angle ABC = 45^\circ $. Construct a similar triangle $ A'B'C' $ whose corresponding sides are $ \frac{3}{4} $ of the sides of $ \triangle ABC $. Write the steps of construction in brief.

In the figure, if $ BD \perp AC $ and $ CE \perp AB $, prove that $ \triangle AEC \sim \triangle ADB $.

If the corresponding sides of two similar triangles are in the ratio 3:5, the ratio of their areas will be:

If the sides of a triangle are 3 cm, 4 cm and 5 cm, then the triangle will be:

The perimeter of two similar triangles are 10 cm and 15 cm respectively, find the ratio of their areas.

Two figures whose shapes are same but the dimensions are not essentially same are called:

Construct a triangle of sides 4 cm, 5 cm, and 6 cm, and again construct another corresponding triangle whose sides are $ \frac{2}{3} $ of the corresponding sides of the previous triangle.

In a right triangle $ ABC $, angle $ B $ is a right angle and $ BD $ is perpendicular on $ AC $. Prove that: $ AB^2 = AC \cdot AD $.

A perpendicular is drawn from the vertex to the base of an equilateral triangle of side a. The measure of the perpendicular will be:

The median of side AB of an equilateral triangle ABC is CD. The value of $ CD^2 $ will be:

The areas of two similar triangles are in the ratio 81:121. The ratio of their sides will be:

Draw a line segment of length 76 cm and divide it in the ratio 3:4. Write the measures of both the two parts.

In the figure, $ AB = 3 $ cm, $ AC = 6 $ cm, $ BD = 2 $ cm and $ CD = 4 $ cm. The ratio of $ \angle BAD $ and $ \angle CAD $ will be:

If the circumference and the area of a circle are numerically equal, the radius of the circle will be:

In the given figure, if $PQ : BC = 1 : 3$, then the ratio of $AP : PB$ will be: