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 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:
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.
Given: A circle with centre O and AB its diameter, AC is a chord such that ∠BAC = 30°.
To Prove: BC = BD
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
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.
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 ÐAEC.
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 ΔABC in which AB = AC = 6 cm, is inscribed in a circle of radius 9 cm, find the area of the triangle.
Given that an isosceles DABC is inscribed in a circle with centre O and radius 9 cm.
Join OB, OC and OA.