Practice Exercise on Geometry and Mensuration

In the figure given, what is the measure of ∠ACD?

Two circles C₁ and C₂ of radius 2 and 3 respectively touch each other as shown in the figure. If AD and BD are tangents then the length of BD is

If the sides of a triangle measure 13, 14, 15 cm respectively, what is the height of the triangle for the base side 14?

A right angled triangle is drawn on a plane such that sides adjacent to the right angle are 3 cm and 4 cm. Now three semi-circles are drawn taking all three sides of the triangle as diameters respectively (as shown in the figure). What is the area of the shaded regions A₁ + A₂?

A lateral side of an isosceles triangle is 15 cm and the altitude is 8 cm. What is the radius of the circumscribed circle?

Let a, b, c be the lengths of the sides of triangle ABC. Given (a + b + c)(b + c − a) = αbc. Then the value of α will lie in between

In the figure given below (not drawn to scale), A, B and C are three points on a circle with centre O. The chord BC is extended to point T such that AT becomes a tangent to the circle at point A. If ∠CTA = 35° and ∠CAT = 45°, calculate x° (∠BOC).

In the given figure, AB = 20, BC = 15, CA = 19. Calculate a, b, c.

In the given figure, AB = 20, BC = 15, CA = 19. Calculate a, b, c.

The angle between lines L and M measures 35°. If line M is rotated 45° counter-clockwise about point P to line M¹, what is the angle in degrees between lines L and M¹?