Question

prove that the tangent drawn from an external point to a circle (1) are equal. (2) subtend equal angles are the centre

Answer 1

I hope it will help you.

Answer 2

AC andBCare the tangents drawn from an external point C to the circle with centre O
In triangle OAC and triangle OBC
OA=OB (radii of the same circle)
angleOAC=angle OBC=90°(radius is perpendicular to tangent)
OC-common side
Therefore, Triangle OAC is congruent to triangle OBC
Therefore,
AC=BC [By
Angle AOC=angle BOC CPCT]
Therefore, tangents drawn from a common external point to a circle is equal and they subtend equal angles at the center
Thank you