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

In the given figure ABC is a triangle. CP bisects angle ACB and MN is perpendicular bisector of BC. MN cuts CP at Q. Prove Q is equidistant from B and C, and also that Q is equidistant from BC and AC. 

A and B are fixed points while Pis a moving point, moving in a way that it is always equidistant from A and B. What is the locus of the path traced out by the pcint P? 

In given figure, ABCD is a kite. AB = AD and BC =CD. Prove that the diagona AC is the perpendirular bisector of the diagonal BD. 

In given figure 1 ABCD is an arrowhead. AB = AD and BC = CD. Prove th at AC produced bisects BD at right angles at the point M

In Δ PQR, bisectors of  ∠ PQR and ∠ PRQ meet at I. Prove that I is equidistant from the three sides of the triangle , and PI bisects ∠ QPR . 

In Δ ABC, B and Care fixed points. Find the locus of point A which moves such that the area of Δ ABC remains the same. 

Draw and describe the lorus in  the following cases: 

The locus of points at a distance of 4 cm from a fixed line. 

Draw and describe the locus in the following case:

The locus of points inside a circle and equidistant from two fixed points on the circle.

Draw and describe the lorus in the following cases: 

The Iocus of the mid-points of all parallel chords of a circle.

Draw and describe the locus in the following case:

The locus of a point in rhombus ABCD which is equidistant from AB and AD.

Describe completely the locus of a point in the following case:

Midpoint of radii of a circle. 

Describe completely the locus of a point in the following case:

Centre of a ball, rolling along a straight line on a level floor. 

Describe completely the locus of a point in the following case:

Point in a plane equidistant from a given line. 

Prove the following identity : 

`1/(cosA + sinA - 1) + 2/(cosA + sinA + 1) = cosecA + secA`

Describe completely the locus of a point in the following case:

Centre of a circle of varying radius and touching the two arms of ∠ ABC. 

Describe completely the locus of a point in the following case:

Centre of a circle of radius 2 cm and touching a fixed circle of radius 3 cm with centre O. 

Using only ruler and compasses, construct a triangle ABC 1 with AB = 5 cm, BC = 3.5 cm and AC= 4 cm. Mark a point P, which is equidistant from AB, BC and also from Band C. Measure the length of PB. 

Construct a triangle ABC, such that AB= 6 cm, BC= 7.3 cm and CA= 5.2 cm. Locate a point which is equidistant from A, B and C.

Prove the following identity : 

`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (cosA + 1)/sinA`

Prove the following identity : 

`(cosecθ)/(tanθ + cotθ) = cosθ`