At Saralstudy, we are providing you with the solution of Class 10 Mathematics Circles according to the latest NCERT (CBSE) Book guidelines prepared by expert teachers. Here we are trying to give you a detailed answer to the questions of the entire topic of this chapter so that you can get more marks in your examinations by preparing the answers based on this lesson. We are trying our best to give you detailed answers to all the questions of all the topics of Class 10 Mathematics Circles so that you can prepare for the exam according to your own pace and your speed.
Circle is the locus of points equidistant from a given point, which is the centre of the circle. And, tangent is the line which intersects a circle at one point only. On these points which touches at only one point. Hence, a circle can have infinite tangents.
In the given figure , AB and BC are two parallel lines. The line segment BC is the tangent at point x while AB is the secant to the circle.
Diagram drawn according to the question. Here OP is the radius of the circle.
Given : A quadrilateral ABCD which circumscribe a circle .
To prove: AB + CD = AD + BC
Proof: As we know tangents drawn from external point are equal. Therefore, we have
DR = DS …………….. (1)
AP = AS ……………… (2)
PB = BQ ……………… (3)
CR = CQ ………………. (4)
Adding equation (1), (2), (3) and (4), we get
DR + AP + PB + CQ = DS + AS + BQ + CR
AB + CD = AD + BC
Hence proved.
Exercise 2 ( Page No. : 214 )
