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ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 16 Symmetry Reflection and Rotation

Question 1.
Draw the line or lines of symmetry, if any, of the following shapes and count their number:

Solution:

Question 2.
For each of the given shape in question 1, find the order of the rotational symmetry (if any).
Solution:

Question 3.
Construct a rectangle ABCD such that AB = 4.5 cm and BC = 3 cm. Draw its line (or lines) of symmetry.
Solution:

Question 4.
Construct a rhombus ABCD with AB = 5.3 cm and ∠A = 60°. Draw its line (or lines) of symmetry.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 15 Circle Check Your Progress

Question 1.
Draw a circle of radius 2·7 cm. Draw a chord PQ of length 4 cm of this circle. Shade the major segment of this circle.
Solution:

Question 2.
Draw a circle of radius 3·2 cm and in it make a sector of angle.
(i) 30°
(ii) 135°
(iii) \(2 \frac{2}{3}\) right angles
Draw separate diagrams and shade the sectors.
Solution:

Question 3.
Draw a line segment PQ = 6·4 cm. Construct a circle on PQ as diameter. Take any point R on this circle and measure ∠PRQ.
Solution:

Question 4.
In the adjoining figure, the tangent to a circle of radius 6 cm from an external point P is of length 8 cm. Calculate the distance of the point P from the nearest point of the circumference.

Solution:

Question 5.
In the given figure, O is the centre of the circle. If ∠ABP = 35° and ∠BAQ = 65°, find
(i) ∠PAB
(ii) ∠QBA

Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

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 endpoints ……………
(ii) A diameter of a circle is a chord that …………… the centre of the circle.
(iii) A line meets a circle almost 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:

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:

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:

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:

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:

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:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 15 Circle

Question 1.
Draw a circle with centre O and radius 2.5 cm. Draw two radii OA and OB such that ∠ AOB = 60°. Measure the length of the chord AB.
Solution:

Question 2.
Draw a circle of radius 3·2 cm. Draw a chord AB of this circle such that AB = 5 cm. Shade the minor segment of the circle.
Solution:

Question 3.
Find the length of the tangent drawn to a circle of radius 3 cm, from a point at a distance 5 cm from the centre.
Solution:

Question 4.
In the adjoining figure, PT is a tangent to the circle with centre C. Given CP = 20 cm and PT = 16 cm, find the radius of the circle.

Solution:

Question 5.
In each of the following figure, O is the centre of the circle. Find the size of each lettered angle :

Solution:

Question 6.
In each of the following figures, O is the j centre of the circle. Find the values of x and y.

Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Check Your Progress

Question 1.
Construct a quadrilateral ABCD such that AB = 4·5 cm, BC = 4 cm, CD = 3·9 cm, AD = 3·2 cm and ∠B = 60°.
Solution:

Question 2.
Construct a quadrilateral ABCD such that AB = 5 cm, BC = 4·2 cm, AD = 3·5 cm, ∠A = 90°, ∠B = 60°.
Solution:

Question 3.
Construct a quadrilateral ABCD in which AB 3·5 cm, BC = 5 cm, CD = 5·6 cm, DA = 4 cm and BD = 5·4 cm
Solution:

Question 4.
Construct a quadrilateral PQRS in which PQ = 3 cm, QR = 2·5 cm, PS = 3·5 cm, PR = 4 cm and QS = 5 cm.
Solution:

Question 5.
Construct a quadrilateral ABCD given that BC = 6 cm, CD = 4 cm, ∠B = 45°, ∠C = 90° and ∠D = 120°.
Solution:

Question 6.
Construct a parallelogram ABCD in which AB = 5.2 cm, AC = 6.5 cm and BD = 7.8 cm.
Solution:

Question 7.
Construct a parallelogram ABCD in which diagonal AC = 4 cm, diagonal BD = 6 cm and angle between diagonals is 75°.
Solution:

Question 8.
Construct a rectangle PQRS such that PQ = 3·5 cm and ∠RPS = 75°.
Solution:

Question 9.
Construct a rectangle whose one diagonal is 6-8 cm and an angle between two diagonals is 105°.
Solution:

Question 10.
Construct a rhombus BEST such that BE = 4.5 cm, ET = 6 cm.
Solution:

Question 11.
Construct a rhombus whose diagonals are 7 cm and 5·3 cm.
Solution:

Question 12.
Construct a square whose one diagonal is 5·8 cm.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths