(English Medium) ICSE Class 9 - CISCE Question Bank Solutions

The given figure shows a parallelogram ABCD with area 324 sq. cm. P is a point in AB such that AP: PB = 1:2
Find The area of Δ APD.

In parallelogram ABCD, E is a point in AB and DE meets diagonal AC at point F. If DF: FE = 5:3 and area of  ΔADF is 60 cm²; find
(i) area of ΔADE.
(ii) if AE: EB = 4:5, find the area of  ΔADB.
(iii) also, find the area of parallelogram ABCD.

In ΔABC, E and F are mid-points of sides AB and AC respectively. If BF and CE intersect each other at point O,
prove that the ΔOBC and quadrilateral AEOF are equal in area.

The figure given below shows a circle with center O in which diameter AB bisects the chord CD at point E. If CE = ED = 8 cm and EB = 4 cm,
find the radius of the circle.

In parallelogram ABCD, P is the mid-point of AB. CP and BD intersect each other at point O. If the area of ΔPOB = 40 cm², and OP: OC = 1:2, find:
(i) Areas of ΔBOC and ΔPBC
(ii) Areas of ΔABC and parallelogram ABCD.

In the following figure, OABC is a square. A circle is drawn with O as centre which meets OC at P and OA at Q.
Prove that:
( i ) ΔOPA ≅ ΔOQC 
( ii ) ΔBPC ≅ ΔBQA

Draw two circles of different radii. How many points these circles can have in common? What is the maximum number of common points?

Suppose you are given a circle. Describe a method by which you can find the center of this circle.

State, the following variable is continuous or discrete:
number of children in your class.

State, the following variable is continuous or discrete:
Distance travelled by car.

State, the following variable is continuous or discrete:
Sizes of shoes.

State, the following variable is continuous or discrete: Time.

State, the following variable is continuous or discrete: Number of patients in a hospital.

Show that:

The ratio of the areas of two triangles of the same height is equal to the ratio of their bases.

Show that:
The ratio of the areas of two triangles on the same base is equal to the ratio of their heights.

Fill in the blank :
 A quantity which can very from one individual to another is called a ............. 

Fill in the blank :
Sizes of shoes are ........... variables.

Fill in the blank :
Daily temperatures is ........... variable.

Find the mean of x + 3, x + 5, x + 7, x + 9 and x + 11.

The mean of 15 observations is 32. Find the resulting mean, if the observation is: Increased by 3