Multiple choice

Two tangent segments BC, BD are drawn to a circle C (O, r) such that $\angle D B C = 120 ^ { 0 }$. then $\mathrm { BO } = \mathrm { BC }$.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In the triangle formed by the center O and the tangents, the angle at the center is 180 - 120 = 60 degrees. Since the triangle OBC is a right triangle at C, the angle BOC is 60 degrees, making it an equilateral triangle or using trigonometry, BC = BO * tan(60). The statement BO = BC is false.

AI explanation

The radius to a tangent is perpendicular to the tangent line, creating right angles at points B and D in quadrilateral OBDC. The line BO bisects the 120 degree angle, making angle OBC 60 degrees and leaving angle BOC at 30 degrees. In triangle BOC, the side BC is opposite the 30 degree angle and BO is opposite the 90 degree angle, so their lengths are not equal; the statement is false.

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