Question

Given that two tangent lines are constructed from the shared point A outside a circle to the points of tangency B and C, what is the relationship between AB and AC?

Answer 1

AB ≅ AC

The tangent lines are congruent.

Answer 2

Given that there are two tangent lines AB and AC which are constructed from the shared point A outside a circle to the points of tangency B and C.

Now we have to find the relationship between AB and AC.

We know that any tangent line to the circle makes right angle with the radius at the point of tangency.

So both tangent lines AB and AC will be perpendicular to the radius.

radius is always equal so OA=OB

now join the point A with center O of the circle.

This will form two congruent triangles having two equal radii OA and OB, common side OA and right angle

Due to congurency of the triangles, both sides AB and AC will be equal

Hence final answer is AB=AC.