Here you get the CBSE Class 10 Mathematics chapter 9, Circles: NCERT Exemplar Problems and Solutions (Part-IIA). This part of the chapter includes solutions to Question Number 1 to 5 from Exercise 9.2 of NCERT Exemplar Problems for Class 10 Mathematics Chapter: Circles. This exercise comprises only the Very 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:
Very Short Answer Type Questions (Q. No. 1-5)
Questions. 1 If a chord AB subtends an angle of 60° at the centre of a circle, then angle between the tangents at A and B is also 60°.
Given conditions can be expressed in the form of following diagram:
We know that a tangent at any point on a circle is perpendicular to the radius through the point of contact.
Questions. 2 The length of tangent from an external point P on a circle is always greater than the radius of the circle.
The length of a tangent from an external point may or may not be greater than the radius of the circle.
It can be clear from the following diagrams:
Questions. 3 The length of tangent from an external point P on a circle with centre O is always less than OP.
Let PT be a tangent at point T lying on a circle with centre O. Join OT.
As, in a right angled triangle, hypotenuse is always greater than any of the two sides of the triangle.
∴ OP > PT
or PT < OP
Hence, the length of tangent from an external point P on a circle with centre O is always less than OP.
Questions. 4 The angle between two tangents to a circle may be 0°.
Angle between two tangents to a circle will be 0° only when the two tangents will coincide with each other or will be parallel to each other.
Questions. 5 If angle between two tangents drawn from a point P to a circle of radius a and centre O is 90°, then.
Given condition can be represented as given in the following diagram:
We know that any two tangents drawn to a circle from an external point are equally inclined to the line segment, joining the centre to that point.