CMAT Geometry Practice Questions With Solutions

In a $\triangle PQR$ , point Xis on PQ and point Y is on PR such that XP = 1.5 units, XQ = 6 units, PY= 2 units and YR = 8 units. Consider the following statements :
Statement I : QR = 5 XY
Statement II :$\triangle PYX$ is similar to $\triangle PRQ$
In the light of the above statements, choose the correct answer from the options given below.

Given below are two statements:

Statement II : If the circumference and the area of a circle are numerical equal, then
the diameter is equal to 4.

The length of a rectangle is increased by 25%. By what percent should its breadth be decreased so as to maintain the same area ?

Given below are two statements :
Statement I : The perimeter of a triangle is greater than the sum of its three medians.
Statement II : In any triangle ABC, if D is any point on BC, then AB + BC + CA > 2AD.
In the light of the above statements, choose the correct answer from the options given below :

Given below are two statements :
Statement I: If two chords XY and ZT of a circle intersects internally at point P, then PX - PY = PZ - PT
Statement II: If two chords XY and ZT of a circle intersect internally at point P, then PXZ and PTY are similar triangles.
In the light of the above statements, choose the correct answer from the options given below:

Given below are two statements :
Statement I: The perimeter of a triangle is greater than the sum of its three medians.
Statement II: In any triangle ABC, if D is any point on BC, then AB + BC + CA > 2 AD.
In the light of the above statements, choose the correct answer from the options given below :

A cylindrical vessel of radius 4 cm contains water. A solid sphere of 3 cm radius is lowered into the water until it is completely immersed . The water level in the vessel will rise by :

What is the area of an equilateral triangle whose inscribed circle has radius R?

In the following diagram, if the shaded area is one half the area of triangle ABC and angle ABC is right angle then the length of line segment AD is

A copper wire having length of 243m and diameter 4 mm was melted to form a sphere. Find the diameter of the sphere :