Question

In the given figure, AB and CD are tangents to a circle centred at O. Is ∠BAC = ∠DCA? Justify your answer. 

Answer 1

To prove ∠BAC = ∠DCA

Construction: Join OC and OA 

Now,

∠OAB = ∠OCD = 90°  ...(i)

In ∆AOC

OC = OA (radius of circle)

∴ ∠OAC = ∠OCA   ...(ii)

Adding equation i and ii

∠OAB + ∠OAC = ∠OCD + ∠OCA

∠BAC = ∠DCA

Proved.