Here you get the CBSE Class 10 Mathematics chapter 9, Circles: NCERT Exemplar Problems and Solutions (Part-IVB). This part of the chapter includes solutions to Question Number 8 to 14 from Exercise 9.4 of NCERT Exemplar Problems for Class 10 Mathematics Chapter: Circles. This exercise comprises only the Long Answer Type Questions framed from various important topics in the chapter.

For solutions to questions 1 to 7, check the following link:

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

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 9.4**

**Long Answer Type Questions**** (Q. No. 8-14)**

**Question. 8 ***AB *is a diameter and *AC *is a chord of a circle with centre *O *such that ∠*BAC *= 30°. The tangent at *C *intersects extended *AB *at a point *D. *Prove that *BC = BD.*

**Solution.**

**Given: **A circle with centre *O* and *AB *its diameter, *AC *is a chord such that ∠*BAC* = 30°.

**T****o Prove: ***BC = BD*

**Proof: **

We know that the angle between tangent and the chord equals angle made by the chord in alternate segment.

**Question. 9 **Prove that the tangent drawn at the mid point of an arc of a circle is parallel to the chord joining the end points of the arc

**Solution.**

Given: Consider an arc *ACB *in which *C* is mid point of arc *ACB* and *PCQ* is the tangent to the circle.

Join *AC*, *BC* and *AB*.

**Question. 10** In a figure the common tangents, *AB *and *CD *to two circles with centres *O *and *O*’ intersect at *E.*

Prove that the points *O, E *and *O*’ are collinear.

**Solution.**

**Given: ***AB* and *CD* are the two common tangents to two circles with centres *O* and *O*’.

*AB* and *CD* intersect at *E*.

**To prove:** Points *O, E *and *O*’ are collinear

**Construction:** Joint *AO, OC *and *O’D, O’B*

Similarly, *OE *is the angle bisector of Ð*AEC**.*

**Question. 11 **In figure, *O *is the centre of a circle of radius 5 cm, *T *is a point such that *OT *= 13 and *OT*

intersects the circle at *E, *if *AB *is the tangent to the circle at *E*, find the length of *AB.*

**Question. 12 **The tangent at a point *C* of a circle and a diameter *AB *when extended intersect at *P*. If ∠*PCA =*

110°, find ∠*CBA.*

[Hint: Join *C* with centre *O*].

But angle between tangent and the chord equals the angle made by the chord in alternate segment

**Question. 13 **If an isosceles Δ*ABC *in which *AB = AC = *6* *cm, is inscribed in a circle of radius 9 cm, find the area of the triangle.

**Solution.**

Given that an isosceles D*ABC *is inscribed in a circle with centre *O * and radius 9 cm.

Join *OB, OC *and *OA.*

**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**