Question

In the figure. I and m are two parallel tangents to a circle with centre 0, touching the
circle at A and B respectively. Another tangent at C intersects the line l at D and m at e
Prove that ZDOE = 90°​

Answer 1

Answer:

hope this will help you

Step-by-step explanation:

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.