Master Class 10 Maths Circles Ex 10.2 CBSE Ex 11.2 SEBA

Class 10 Maths Circles Ex 10.2 CBSE Ex 11.2 SEBA deals with problems based on the length of tangents drawn from an external point to a circle. This exercise involves applying theorems related to tangents, such as the property that tangents drawn from an external point are equal in length. Students will solve questions involving constructions, diagrams, and use of the Pythagoras theorem. It helps in strengthening geometric understanding and improves the ability to apply theorems in solving real-world problems related to circles.

Class 10 Maths Circles Ex 10.2 CBSE Ex 11.2 SEBA

Question 1.
From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is
(a) 7 cm
(b) 12 cm
(c) 15 cm
(d) 24.5 cm
Solution:
Ex 10.2 Class 10 Maths Solutions NCERT PDF Q1

Ex 10.2 Class 10 Maths Question 2.
In figure, if TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110°, then ∠PTQ is equal to
(a) 60°
(b) 70°
(c) 80°
(d) 90°
NCERT Solutions for Class 10 Maths Chapter 10 Circles Ex 10.2 Q1
Solution:
Ex 10.2 Class 10 Maths Solutions NCERT PDF Q2

Ex 10.2 Class 10 Maths Question 3.
If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 80°, then ∠POA is equal to
(a) 50°
(b) 60°
(c) 70°
(d) 80°
Solution:
Ex 10.2 Class 10 Maths Solutions NCERT PDF Q3

Ex 10.2 Class 10 Maths Question 4.
Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
Solution:
Exercise 10.2 Class 10 Maths Solutions NCERT PDF Q4

Ex 10.2 Class 10 Maths Question 5.
Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.
Solution:
Exercise 10.2 Class 10 Maths Solutions NCERT PDF Q5

Ex 10.2 Class 10 Maths Question 6.
The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.
Solution:
Exercise 10.2 Class 10 Maths Solutions NCERT PDF Q6

Ex 10.2 Class 10 Maths Question 7.
Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.
Solution:
Circles Class 10 NCERT Solutions Ex 10.2 PDF Q7

Ex 10.2 Class 10 Maths Question 8.
A quadrilateral ABCD is drawn to circumscribe a circle (see figure). Prove that AB + CD = AD + BC.
NCERT Solutions for Class 10 Maths Chapter 10 Circles Ex 10.2 Q8
Solution:
Circles Class 10 NCERT Solutions Ex 10.2 PDF Q8

Ex 10.2 Class 10 Maths Question 9.
In figure, XY and X’Y’ are two parallel tangents to a circle , x with centre O and another tangent AB with point of contact C intersecting XY at A and X’Y’ at B. Prove that ∠AOB = 90°.

Solution:

Ex 10.2 Class 10 Maths Question 10.
Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining the points of contact at the centre.
Solution:
Chapter 10 Maths Class 10 NCERT Solutions Ex 10.2 PDF Q10

Ex 10.2 Class 10 Maths Question 11.
Prove that the parallelogram circumscribing a circle is a rhombus.
Solution:

Ex 10.2 Class 10 Maths Question 12.
A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively (see figure). Find the sides AB and AC.

Solution:

Ex 10.2 Class 10 Maths Question 13.
Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
Solution: