# Question Video: Finding the Size of an Angle in a Triangle given the Other Two Anglesβ Sizes Using the Properties of Tangents Mathematics • 11th Grade

π΅πΆ is tangent to the circle π at π΅. Find πβ π΄π΅πΆ.

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### Video Transcript

π΅πΆ is tangent to the circle π at π΅. Find the measure of the angle π΄π΅πΆ.

In order to calculate the angle π΄π΅πΆ, we firstly need to consider the triangle π΄π΅π. The length π΄π is equal to the length ππ΅ as they are both radii of the circle. This means that triangle π΄π΅π is isosceles. As the triangle is isosceles, angle ππ΄π΅ is equal to angle ππ΅π΄. Both of these angles are equal to 33 degrees.

As π΅πΆ is a tangent, then we can see that π΅πΆ meets π΅π at 90 degrees. A tangent will always meet the radius at 90 degrees. This means that π plus 33 must be equal to 90. Subtracting 33 from both sides of this equation gives us π equals 57.

This means that the measure of angle π΄π΅πΆ is equal to 57 degrees.