Question
Mathematics Question on Number of Tangents from a Point on a Circle
A quadrilateral ABCD is drawn to circumscribe a circle (see Fig. 10.12). Prove that AB + CD = AD + BC
Fig. 10.12
Answer
It can be observed that
DR = DS (Tangents on the circle from point D) .....… (1)
CR = CQ (Tangents on the circle from point C) ......… (2)
BP = BQ (Tangents on the circle from point B) …..… (3)
AP = AS (Tangents on the circle from point A) …..… (4)
Adding all these equations, we obtain
DR + CR + BP + AP = DS + CQ + BQ + AS
(DR + CR) + (BP + AP) = (DS + AS) + (CQ + BQ)
CD + AB = AD + BC