Since AC is tangent to circle O at A, we know that ∠YAC is equal to the angle subtended by arc AY (the arc formed by points A and Y on the circle) at point Y.
Since arc AY is outside the circle and angle BY is an inscribed angle subtended by the same arc, we can use the Inscribed Angle Theorem to find that m∠BY = 1/2 * m(arc AY) = 52°.
Therefore, m(arc AY) = 2 * m∠BY = 2 * 52° = 104°.
Since ∠YAC is the angle subtended by the same arc AY, we have that m∠YAC = m(arc AY) = 104°.
Therefore, m∠YAC = 104°.
AC is tangent to circle O at A.
If mBY=52°, what is m∡YAC?
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