47annakendrickx 47annakendrickx

17-03-2019
Mathematics

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AB and AC are tangent segments of circle k(O). What is the measure of the angle ∠BAC, if midpoint of AO lies on the circle k(O)?
m∠BAC=

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sqdancefan sqdancefan

17-03-2019

Answer:

60°

Step-by-step explanation:

B and C are the points of intersection of the circle with diameter AO with circle O. If the midpoint of AO is X on circle O, then XO = XB = XC and ΔXOB and ΔXOC are equilateral triangles. That makes ∠BOC = 120° and its supplement, ∠BAC, equal to 60°.

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