Question

As shown in figure, AD, AE and BC are tangents to the circle at a point D, E and F respectively, then
(A) AD = AB + BC + CA
(C) BAD = AB + BC + CA
(B) 2AD = AB + BC + CA
(D) 4AD = AB + BC + CA
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Answer 1

It is given that ∠BAD=∠EAC

∠BAD+∠DAC=∠EAC+∠DAC [add ∠DAC on both sides]

∴∠BAC=∠DAE

In △BAC and △DAE

AB=AD (Given)

∠BAC=∠DAE (Proved above)

AC=AE (Given)

∴△BAC≅△DAE (By SAS congruence rule)

∴BC=DE (By CPCT)