CBSE Class 10 Answered
Let us consider a circle centred at point O. Let P be a external point from which two tangents PA and PB are drawn to circle which are touching circle at point A and B respectively and AB is the line segment, joining point of contacts A and B together such that it subtends AOB at centre O of circle.
Now we may observe that:
OA (radius) PA (tangent)
So, OAP = 90o
Similarly, OB (radius) PB (tangent)
OBP = 90o
Now in quadrilateral OAPB, sum of all interior angles = 360o
OAP + APB + PBO +BOA = 360o
90o + APB + 90o + BOA = 360o
APB +BOA = 180o
Hence, the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.