Question

1. In the following figure, l and m are two parallel tangents to a circle with centre O, touching the

circle at A and B respectively. Another tangent at C intersects the line l at D and m at E. prove that

∠DOE = 90º.​

Answer 1

Answer:

Join OC

In triangle ODA and triangle ODC

OA=OC (Radii of the same circle )

AD=DC (Length of tangent drawn from an external point to a circle are equal)

DO=OD (common side)

ΔDOA≅ΔODC

∴∠DOA=∠COD

ΔDOA≅ΔODC

∴∠DOA=∠COD

Similarly ΔOEB≅ΔOEC

∴∠EOB=∠COE

AOB is a diameter of the circle.

Hence, it is a straight line.

∴∠DOA+∠COD+∠COE+∠EOB=180

⇒2∠COD+2∠COE=180

⇒∠COD+∠COE=90

⇒∠DOE=90

0

Hence proved.