Here you get the CBSE Class 10 Mathematics chapter 9, Circles: NCERT Exemplar Problems and Solutions (Part-IIB). In this part you will get solutions to Question Number 6 to 10 from exercise 9.2 of NCERT Exemplar Problems for Class 10 Mathematics Chapter: Circles. Each solution is designed to give you an apt explanation and that too in simple steps. For solutions to Question Number 1 to 5 of exercise 9.2, check the following link:

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

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 9.2**

**Very Short Answer Type Questions**** (Q. No. 6-10)**

**Question. 7 **The tangent to the circumcircle of an isosceles Δ*ABC *at *A, *in which *AB* = *AC, *is parallel to *BC.*

**Solution. True**

Let *DE* be the tangent to the circumcircle of an isosceles Δ*ABC *at *A*.

**Question. 8 **If a number of circles touch a given line segment *PQ *at a point *A, *then their centres lie on the perpendicular bisector of *PQ.*

**Solution. False**

Let circles *S*_{1}, *S*_{2}, *S*_{3}, *S*_{4}, ... with centres *C*_{1}, *C*_{2}, *C*_{3}, *C*_{4}, ..., respectively, touch the line segment *PQ *at a point *A. *

We know that perpendicular on any point of a segment *PQ* may be only one. Therefore, all the line segments *C*_{1}*A, C _{2}A. C_{3}A,*...,

*so on are coincident.*

But as *A* is not mid point of *PQ *therefore, perpendicular *AB* will not be the perpendicular bisector of *PQ*.

Thus, the centre of each circle lies on a line segment which is perpendicular to *PQ* but not its bisector.

**Question. 9 **If a number of circles pass through the end points *P *and Q of a line segment *PQ, *then their centres lie

on the perpendicular bisector of PQ.

**Solution. True**

Let *S*_{1}, *S*_{2} and *S*_{3 } be the circles with centres *C*_{1}, *C*_{2 }and_{ }*C*_{3}, respectively,* _{ }*passing through the end points

*P*and Q of a line segment

*PQ.*

** **

As we know that the perpendicular bisectors of a chord of a circle always passes through the centre of circle.

Thus, perpendicular bisector of *PQ *passes through *C*_{1}, *C*_{2 }and_{ }*C*_{3}. Similarly, all the circle passing through *PQ *will have their centre on perpendiculars bisectors of *PQ.*

**Question. 10 ***AB *is a diameter of a circle and *AC *is its chord such that *Ð** BAC *= 30°. If the tangent at *C *intersects *A *extended at *D, *then *BC = BD.*

**Solution. True**

Consider the following diagram:

**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**

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