Here you get the CBSE Class 10 Mathematics chapter 9, Circles: NCERT Exemplar Problems and Solutions (Part-IIIB). This part of the chapter includes solutions to Question Number 6 to 10 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:
Short Answer Type Questions (Q. No. 6-10)
Question. 6 In figure, AB and CD are common tangents to two circles of equal radii. Prove that AB = CD.
Given: Two circles of equal radii, two common tangents, AB and CD on circles C1 and C2 with centres O1 and O2.
To prove: AB = CD
Construction: Join AC, BD, O2A, O2C, O2B, O2D, O1A and O1C.
Question. 7 In figure, common tangents AB and CD to two circles intersect at E. Prove that AB = CD.
Question. 8 A chord PQ of a circle is parallel to the tangent drawn at a point R of the circle. Prove that R bisects the arc PRQ.
Given: Chord PQ of a circle is parallel to tangent drawn at point R of that circle.
Question. 9 Prove that the tangents drawn at the ends of a chord of a circle make equal angles with the chord.
Given: Two tangents are drawn at the ends of the chord of a circle.
To prove: ∠1 = ∠2
Let two tangents drawn at the ends of a chord AB intersect at point C.
As, we know that tangents drawn from an external point to a circle are equal,
∴ AC = BC
⟹ ∠2 = ∠1 [Angles opposite to equal sides of a triangle are equal]
Hence, tangents AC and BC make equal angles with chord AB.
Question. 10 Prove that a diameter AB of a circle bisects all those chords which are parallel to the tangent at the point A.
Given: AB is a diameter of the circle with centre O and a chord CD is parallel to tangent MAN .
Now, we know that a perpendicular drawn from centre of circle to chord bisects the chord.
Thus, OE bisects CD.
Similarly, the diameter AB bisects all the chords which are parallel to the tangent at the point A.