(English Medium) ICSE Class 10 - CISCE Question Bank Solutions

Find the sum of all multiples of 7 lying between 300 and 700.

The sum of n natural numbers is 5n² + 4n. Find its 8^th term.

The fourth term of an A.P. is 11 and the eighth term exceeds twice the fourth term by 5. Find the A.P. and the sum of first 50 terms.

Construct a triangle ABC, in which AB = 4.2 cm, BC = 6.3 cm and AC = 5 cm. Draw perpendicular bisector of BC which meets AC at point D. Prove that D is equidistant from B and C. 

In each of the given figures; PA = PB and QA = QB. 

i.
ii.

Prove, in each case, that PQ (produce, if required) is perpendicular bisector of AB. Hence, state the locus of the points equidistant from two given fixed points.

Construct a right angled triangle PQR, in which ∠Q = 90°, hypotenuse PR = 8 cm and QR = 4.5 cm. Draw bisector of angle PQR and let it meets PR at point T. Prove that T is equidistant from PQ and QR. 

In parallelogram ABCD, side AB is greater than side BC and P is a point in AC such that PB bisects angle B. Prove that P is equidistant from AB and BC. 

In triangle LMN, bisectors of interior angles at L and N intersect each other at point A. Prove that:

1. Point A is equidistant from all the three sides of the triangle.
2. AM bisects angle LMN. 

Use ruler and compasses only for this question.

1. Construct ΔABC, where AB = 3.5 cm, BC = 6 cm and ∠ABC = 60°.
2. Construct the locus of points inside the triangle which are equidistant from BA and BC.
3. Construct the locus of points inside the triangle which are equidistant from B and C.
4. Mark the point P which is equidistant from AB, BC and also equidistant from B and C. Measure and record the length of PB.

The given figure shows a triangle ABC in which AD bisects angle BAC. EG is perpendicular bisector of side AB which intersects AD at point F.

Prove that: 

F is equidistant from A and B.

The given figure shows a triangle ABC in which AD bisects angle BAC. EG is perpendicular bisector of side AB which intersects AD at point F.

Prove that: 

F is equidistant from AB and AC.

The bisectors of ∠B and ∠C of a quadrilateral ABCD intersect each other at point P. Show that P is equidistant from the opposite sides AB and CD. 

Draw a line AB = 6 cm. Draw the locus of all the points which are equidistant from A and B. 

Draw an angle ABC = 75°. Draw the locus of all the points equidistant from AB and BC.

Draw an ∠ABC = 60°, having AB = 4.6 cm and BC = 5 cm. Find a point P equidistant from AB and BC; and also equidistant from A and B. 

In the figure given below, find a point P on CD equidistant from points A and B. 

In the given triangle ABC, find a point P equidistant from AB and AC; and also equidistant from B and C. 

Construct a triangle ABC, with AB = 7 cm, BC = 8 cm and ∠ABC = 60°. Locate by construction the point P such that:

1. P is equidistant from B and C.
2. P is equidistant from AB and BC.
3. Measure and record the length of PB.

Describe the locus for questions 1 to 13 given below:
1. The locus of a point at a distant 3 cm from a fixed point. 

Describe the locus of points at a distance 2 cm from a fixed line.