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.
