NCERT Exemplar Solution for Class 10 Mathematics: Circles (Part-IIIA)

Here you get the CBSE Class 10 Mathematics chapter 9, Circles: NCERT Exemplar Problems and Solutions (Part-IIIA). This part of the chapter includes solutions to Question Number 1 to 5 from Exercise 9.3 of NCERT Exemplar Problems for Class 10 Mathematics Chapter: Circles. This exercise comprises only the Short Answer Type Questions framed from various important topics in the chapter. Each question is provided with a detailed solution.

NCERT exemplar problems are a very good resource for preparing the critical questions like Higher Order Thinking Skill (HOTS) questions. All these questions are very important to prepare for CBSE Class 10 Mathematics Board Examination 2017-2018 as well as other competitive exams.

Find below the NCERT Exemplar problems and their solutions for Class 10 Mathematics Chapter, Circles:

Exercise 9.3

Short Answer Type Questions (Q. No. 1-5)

Question. 1 Out of the two concentric circles, the radius of the outer circle is 5 cm and the chord AC of length 8 cm

is a tangent to the inner circle. Find the radius of the inner circle.

Solution:

Let C₁ and C₂ be the two concentric circles with centre at O. Radius of outer circle C₂ is 5 cm. AC is a 8 cm long chord which touches the inner circle C₁ at point B.

Join OB.

Question. 2 Two tangents PQ and PR are drawn from an external point to a circle with centre O. Prove that QORP is a cyclic quadrilateral.

Solution:

Consider the following diagram:

Question. 3 Prove that the centre of a circle touching two intersecting lines lies on the angle bisector of the lines.

Solution:

Given: Two tangents PQ and PR are drawn from an external point P to a circle with centre O.                                        

To prove: Centre of a circle touching two intersecting lines lies on the angle bisector of the lines.

Construction: Join OR, and OQ.

                                              

Thus, the centre O lies on angle bisecter of PR and PQ.              

Hence proved.

Question. 4 If from an external point B of a circle with centre O, two tangents BC and BD are drawn such that ∠DBC = 120°, prove that BC + BD = BO i.e., BO = 2BC.

Solution:

Given: BD and BC are two tangents drawn from an external point B such that ∠DBC = 120°

Construction: Join OC, OD and OB.

                                    

To prove: BO = 2BC

Proof:

Since, tangent at any point on a circle is perpendicular to the radius through the point of contact,

Question. 5 In figure, AB and CD are common tangents to two circles of unequal radii. Prove that AB = CD

                                                

Solution:

Given: AB and CD are common tangents to two circles of unequal radii.

To prove: AB = CD

                                    

Hence proved.

CBSE Class 10 Mathematics Syllabus 2017-2018

CBSE Class 10 NCERT Textbooks & NCERT Solutions

NCERT Solutions for CBSE Class 10 Maths

NCERT Exemplar Problems and Solutions Class 10 Science: All Chapters