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