## ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 15 Circle Objective Type Questions

**Mental Maths**

Question 1.

Fill in the blanks:

(i) A chord of a circle is a line segment with its end points ……………

(ii) A diameter of a circle is a chord that …………… the centre of circle.

(iii) A line meets a circle atmost in …………… points.

(iv) One-half of the whole arc of a circle is called a …………… of the circle.

(v) The angle subtended by an arc of a circle at the centre of the circle is called the …………… by the arc.

(vi) A line which meets a circle in one and only one point is called a …………… to the circle.

(vii) The tangent at any point of a circle and the radius through that point are …………… to each other.

(viii)From a point outside the circle, …………… tangents can be drawn to the circle.

(ix) The measure of an angle in a semicircle is ……………

Solution:

(i) A chord of a circle is a line segment with its endpoints on the circle.

(ii) A diameter of a circle is a chord that passes through the centre of the circle.

(iii) A line meets a circle almost in two points.

(iv) One-half of the whole arc of a circle is called a semicircle of the circle.

(v) The angle subtended by an arc of a circle at the centre

of the circle is called the angle subtended by the arc.

(vi) A line which meets a circle in one and only

one point is called a tangent to the circle.

(vii) The tangent at any point of a circle and the radius

through that point are perpendicular to each other.

(viii)From a point outside the circle, two tangents can be drawn to the circle.

(ix) The measure of an angle in a semicircle is right angle.

Question 2.

State whether the following statements are true (T) or false (F):

(i) A line segment with its end-points lying on a circle is called a radius of the circle.

(ii) Diameter is the longest chord of the circle.

(iii) The end-points of a diameter of a circle divide the circle into two parts; each part is called a semicircle.

(iv) A diameter of a circle divides the circular region into two parts; each part is called a semicircular region.

(v) The diameters of a circle are concurrent. The centre of the circle is the point common to all diameters.

(vi) Every circle has unique centre and it lies inside the circle.

(vii) Every circle has unique diameter.

(viii)From a given point in the exterior of a circle, two tangents can be drawn to it and these two tangents are equal in length.

Solution:

(i) A line segment with its end-points lying on a

circle is called a radius of the circle. False

Correct:

It is called a chord of the circle.

(ii) Diameter is the longest chord of the circle. True

(iii) The end-points of a diameter of a circle divide the circle

into two parts; each part is called a semicircle. True

(iv) A diameter of a circle divides the circular region

into two parts; each part is called a semicircular region. True

(v) The diameters of a circle are concurrent.

The centre of the circle is the point common to all diameters. True

(vi) Every circle has unique centre and it lies inside the circle. True

(vii) Every circle has unique diameter. False

Correct:

It has infinite number of diameters.

(viii) From a given point in the exterior of a circle,

two tangents can be drawn to it and these two tangents are equal in length. True

**Multiple Choice Questions**

**Choose the correct answer from the given four options (3 to 6):**

Question 3.

If P and Q are any two points on a circle, then the line segment PQ is called a

(a) radius of the circle

(b) diameter of the circle

(c) chord of the circle

(d) secant of the circle

Solution:

P and Q are two points on a circle.

Then line segment PQ is called a chord of the circle. (c)

Question 4.

If P is a point in the interior of a circle with centre O and radius r, then

(a) OP = r

(b) OP > r

(c) OP > r

(d) OP < r

Solution:

P is a point in the interior of a circle with centre O, r is the radius

∴ OP < r (d)

Question 5.

If AB = 12 cm, BC = 16 cm and AB is perpendicular to BC, then the radius of the circle passing through the points A, B and C is

(a) 6 cm

(b) 8 cm

(c) 10 cm

(d) 20 cm

Solution:

AB = 12 cm, BC = 16 cm

AC is the diagonal of ∆ABC

and AC is the diameter of the circle (∵ ∠B = 90°)

Question 6.

In the given figure, AB is a diameter of the circle. If AC = BC, then ∠CAB is equal to

(a) 30°

(b) 45°

(c) 60°

(d) 90°

Solution:

In circle with centre O, AB is its diameter.

∴ ∠C = 90° (Angle in a semi-circle)

By ∠ sum property of ∆

∠A + ∠B +∠C = 180°

∠A + ∠B + 90°= 180°

∴ ∠A + ∠B = 90°

∵ CA = CB

∴ ∠A = ∠B = \(\frac{90^{\circ}}{2}\) = 45°

∴ ∠CAB = 45° (b)