WEBVTT
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𝐵𝐶 is tangent to the circle 𝑀 at 𝐵.
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Find the measure of the angle 𝐴𝐵𝐶.
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In order to calculate the angle 𝐴𝐵𝐶, we firstly need to consider the triangle 𝐴𝐵𝑀.
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The length 𝐴𝑀 is equal to the length 𝑀𝐵 as they are both radii of the circle.
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This means that triangle 𝐴𝐵𝑀 is isosceles.
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As the triangle is isosceles, angle 𝑀𝐴𝐵 is equal to angle 𝑀𝐵𝐴.
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Both of these angles are equal to 33 degrees.
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As 𝐵𝐶 is a tangent, then we can see that 𝐵𝐶 meets 𝐵𝑀 at 90 degrees.
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A tangent will always meet the radius at 90 degrees.
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This means that 𝜃 plus 33 must be equal to 90.
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Subtracting 33 from both sides of this equation gives us 𝜃 equals 57.
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This means that the measure of angle 𝐴𝐵𝐶 is equal to 57 degrees.