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

Prove the following identity : 

`(tanθ + 1/cosθ)^2 + (tanθ - 1/cosθ)^2 = 2((1 + sin^2θ)/(1 - sin^2θ))`

Prove the following identity : 

`(sinA - sinB)/(cosA + cosB) + (cosA - cosB)/(sinA + sinB) = 0`

AB and CD are two intersecting lines. Find a point equidistant from AB and CD, and also at a distance of 1.8 cm from another given line EF. 

Without using set squares or protractor, construct a quadrilateral ABCD in which ∠ BAD = 45°, AD = AB = 6 cm, BC= 3.6 cm and CD=5 cm. Locate the point P on BD which is equidistant from BC and CD. 

Construct a rhombus ABCD with sides of length 5 cm and diagonal AC of length 6 cm. Measure ∠ ABC. Find the point R on AD such that RB = RC. Measure the length of AR. 

Prove the following identity : 

`cosA/(1 - tanA) + sin^2A/(sinA - cosA) = cosA + sinA`

Construct a rhombus ABCD whose diagonals AC and BD are 8 cm and 6 cm respectively. Find by construction a point P equidistant from AB and AD and also from C and D. 

Construct a ti.PQR, in which PQ=S. 5 cm, QR=3. 2 cm and PR=4.8 cm. Draw the locus of a point which moves so that it is always 2.5 cm from Q. 

Construct a Δ XYZ in which XY= 4 cm, YZ = 5 cm and ∠ Y = 1200. Locate a point T such that ∠ YXT is a right angle and Tis equidistant from Y and Z. Measure TZ. 

In  Δ PQR, s is a point on PR such that ∠ PQS = ∠  RQS . Prove thats is equidistant from PQ and QR. 

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.