Two straight lines are drawn through point A, one of which touches the circle at point B.

Two straight lines are drawn through point A, one of which touches the circle at point B. and the second at point C. Prove that AB = AC

Let’s start with what we know from the condition:
o – the center of the circle, in two triangles ABO and AСO;
It is also known that ВO and OС are radii, as well as ВO = OС;
It is also known that:
angle B = angle C;
B, C = 90;
They are equal to 90, because according to the problem AB and AC are tangent, and they are perpendicular to the radius;
AO is the general hypotenuse;
And in the end, if in right-angled triangles some legs and hypotenuse are equal, then the other legs are also equal.

Answer: AB = AC.