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 *C*_{1} and *C*_{2} be the two concentric circles with centre at *O*. Radius of outer circle *C*_{2 }is 5 cm. *AC *is a 8 cm long chord which touches the inner circle *C*_{1} 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 *= 2*BC*.

**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* = 2*BC*

**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**