ICSE ICSE Class 7 - CISCE Question Bank Solutions for Mathematics

In the given figure, prove that: BD = BC.

In the given figure ;
∠1 = ∠2 and AB = AC.
Prove that:
(i) ∠B = ∠C
(ii) BD = DC
(iii) AD is perpendicular to BC.

In the given figure prove that:
(i) PQ = RS
(ii) PS = QR

(i) ∆ XYZ ≅ ∆ XPZ
(ii) YZ = PZ
(iii) ∠YXZ = ∠PXZ

In the given figure, prove that:
(i) ∆ ABC ≅ ∆ DCB
(ii) AC = DB

In the given figure, prove that:

1. ∆AOD ≅ ∆ BOC
2. AD = BC
3. ∠ADB = ∠ACB
4. ∆ADB ≅ ∆ BCA

ABC is an equilateral triangle, AD and BE are perpendiculars to BC and AC respectively. Prove that:
(i) AD = BE
(ii) BD = CE

Use the information given in the following figure to prove triangles ABD and CBD are congruent. Also, find the values of x and y.

The given figure shows a triangle ABC in which AD is perpendicular to side BC and BD = CD. Prove that:
(i) ∆ ABD ≅ ∆ ACD
(ii) AB = AC
(iii) ∠B = ∠C

The radius of a circle is 21 cm. Find the circumference (Take π = `3 1/7`).

The circumference of a circle is 440 cm. Find its radius and diameter. (Take π = `22/7`)

The diameter of a circular field is 56 m. Find its circumference and cost of fencing it at the rate of ₹80 per m. (Take π =`22/7`)

The radius of two circles are 20 cm and 13 cm. Find the difference between their circumferences. (Take π =`22/7`)

The perimeter of a square and the circumference of a circle are equal. If the length of each side of the square is 22 cm, find:
(i) perimeter of the square.
(ii) circumference of the circle.
(iii) radius of the circle.

Find the radius of the circle whose circumference is equal to the sum of the circumferences of the circles having radius 15 cm and 8 cm.

Find the diameter of a circle whose circumference is equal to the sum of circumference of circles with radius 10 cm, 12 cm, and 18 cm.

The circumference of a circle is eigth time the circumference of the circle with a radius of 12 cm. Find its diameter.

The radius of two circles are in the ratio 3 : 5, find the ratio between their circumferences.

The circumferences of two circles are in the ratio 5: 7, find the ratio between their radius.

Each side of a square is 44 cm. Find its perimeter. If this perimeter is equal to the circumference of a circle, find the radius of the circle.