A tangent AB is drawn through point C of the circle centered at O, and AO = OB. Prove that AC = CB.
| April 27, 2021 | education
Since, according to the condition, ОА = ОВ, the triangle AOB is isosceles.
By the property of the tangent drawn to the circle, the radius of the circle drawn to the point of tangency is perpendicular to the tangent. Then OS is the height of triangle AOB, and since triangle AOB is isosceles, then OS is also the median of triangle AOB, and then AC = CB, which was required to prove.
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