NCERT Solutions for Class 10 विज्ञान Chapter 12 Areas Related To Circles

Areas Related To Circles Here is the CBSE विज्ञान Chapter 12 for Class 10 students. Summary and detailed explanation of the lesson, including the definitions of difficult words. All of the exercises and questions and answers from the lesson's back end have been completed. NCERT Solutions for Class 10 विज्ञान Areas Related To Circles Chapter 12 NCERT Solutions for Class 10 विज्ञान Areas Related To Circles Chapter 12 The following is a summary in Hindi and English for the academic year 2025-26. You can save these solutions to your computer or use the Class 10 विज्ञान.

Question 1

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Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts.

Solution

Steps of Construction :
(i) Draw AB = 5.6 cm
(ii) At a draw an acute ∠BAX below base AB.

(iii) On AX make 5 + 8 i.e. 13 equal parts and mark them as A₁, A₂, A₃, A₄,... A₁₃

(iv) Join B to A₁₃. From A₅ draw A₅C || A₁₃B. C is the required point of division and AC : CB = 5 : 8.

On measuring, we get
AC = 3.1 cm,
CB = 4.5 cm
Justification :

$because space space straight A subscript 5 straight C space space space space parallel to space space space straight A subscript 13 straight B therefore space space space fraction numerator AA subscript 5 over denominator straight A subscript 5 straight A subscript 13 end fraction space equals space AC over CB space space space$
[Using basic proportionally theorem]
$But space space space space space fraction numerator AA subscript 5 over denominator straight A subscript 5 straight A subscript 13 end fraction space equals space 5 over 8 space$
Therefore, $AC over CB space equals space 5 over 8 space$

This shows that C divides AB in the ratio 5 : 8.

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NCERT Solutions for Class 10 विज्ञान Chapter 12 Areas Related To Circles

Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts.

Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides arc $2 over 3$ of the corresponding sides of the first triangle.

Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides arc $7 over 5$ of the corresponding sides of the first triangle.

Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another

triangle whose sides are $1 begin inline style 1 half end style$ times the corres ponding sides of the isosceles triangle.

Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ∠ABC = 60°. Then construct a triangle whose sides are $3 over 4$ of the corresponding sides of the triangle ABC.

Draw a triangle ABC with side BC = 7 cm, ∠B = 45°, ∠A = 105°. Then, construct a triangle whose sides are 4/3 times the corresponding sides of ΔABC.

Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm. Then construct another triangle whose sides are $5 over 3$ times the corresponding sides of the given triangle.

Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.

Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actual calculation.

Draw a circle of radius 3 cm. Take two points at a distance 7 cm from its centre. Draw tangents to the circle from these two points P and Q.

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For Daily Free Study Material Join wiredfaculty

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NCERT Solutions for Class 10 विज्ञान Chapter 12 Areas Related To Circles

Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts.

Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides arc of the corresponding sides of the first triangle.

Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides arc of the corresponding sides of the first triangle.

Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are times the corres ponding sides of the isosceles triangle.

Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ∠ABC = 60°. Then construct a triangle whose sides are of the corresponding sides of the triangle ABC.

Draw a triangle ABC with side BC = 7 cm, ∠B = 45°, ∠A = 105°. Then, construct a triangle whose sides are 4/3 times the corresponding sides of ΔABC.

Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm. Then construct another triangle whose sides are times the corresponding sides of the given triangle.

Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.

Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actual calculation.

Draw a circle of radius 3 cm. Take two points at a distance 7 cm from its centre. Draw tangents to the circle from these two points P and Q.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides arc $2 over 3$ of the corresponding sides of the first triangle.

Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides arc $7 over 5$ of the corresponding sides of the first triangle.

Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another

triangle whose sides are $1 begin inline style 1 half end style$ times the corres ponding sides of the isosceles triangle.

Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ∠ABC = 60°. Then construct a triangle whose sides are $3 over 4$ of the corresponding sides of the triangle ABC.

Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm. Then construct another triangle whose sides are $5 over 3$ times the corresponding sides of the given triangle.