CBSE

1. If perimeter of a circle is equal to that of a square, What would be the ratio of their areas.

Here, perimeter of circle = 2πr  and perimeter of square = 4a

∴2

Exercise 11.1

1) Draw a line segment of length 7.6 cm and divide it in 5: 8 ration. In addition, find the measure of two parts.

Solution:

Procedure for construction:

1. Draw any ray AX, making an acute angle with AB.
2. Locate […]
   

1. In the figure, PQ is a chord of a circle and PT is the tangent at P such that ∠QPT = 60°. Then find the measure of ∠PRQ.

Solution.

Since OP is perpendicular to PT.

∠OPT = 90°

∠OPQ = 90°- ∠QPT

∠OPQ = 90 – 60 = 30°.

In ΔOPQ, […]

1. If sun’s elevation is 45°. Find the length of the shadow of a pole of height 8 m.

In rt. Δ PQR, ∠B=90° and ∠

Exercise 8.1

Q1) In △ABC , 90∘ at B, AB=24cm, BC = 7cm.

Determine:

(i)sin(A), cos(A)

(ii) sin(C), cos(C)

Ans.) In

1. If the point A (x , y) is equidistant from B (4 , 2) and C (-2 , 4). Find the relation between x and y.

|AB| = (x−5)

Exercise 1

Question 1:

Fill in the blanks

A: All circles are ________ (Similar, Congruent)

Solution: All circles are similar.

B: All squares are ________ (Congruent, similar)

Solution: All squares are similar.

C: All _________ triangles are similar. (Isosceles, equilateral)

Solution: All equilateral triangles are similar.

D: Two polygons having the same number of sides are similar, if

(i) Their corresponding angles are […]

General Form of an A.P:

Let us consider a series with n number of terms:

a₁ + a₂ + a₃ + a₄ + a₅ + a₆ + a₇ ……………………………..  = a_n

The above series of numbers is said to form an Arithmetic Progression (A.P) if,

a₂ – a₁ = a₃ – a₂ = a₄ – a₃ = …………………………. […]

Polynomials with degree 2 are called quadratic polynomials. When this polynomial is equated to zero, we get a quadratic equation.

Its general form is a² + bx + c = 0, where a, b and c are real numbers and a ≠ 0.

In many real life situations we deal with quadratic equations.

Suppose, we have to make […]

Exercise1 

Question 1:

Astitva tells his daughter, “Seven years ago I was seven times as old as you were then and also three years from now, I shall be three times as old as you will be.”  Represent this situation algebraically and graphically.

Solution:

Let the present age of Astitva be ‘x’.

And, the present age of his daughter be […]