Angle BCD is a circumscribed angle of circle A. What is the measure of angle BCD?
37°, 53°, 74°, 106°

Solution:

∠Given: ∠BAC = 1/2 ∠BAD

∠BAD = 2 × 53 = 106° ----->

since BCD is a circumscribed angle,

∠ABC = 90° and ∠ADC = 90°

The sum of the interior angles in a quadrilateral = 360°

ABC + ∠ADC + BAD + ∠BCD = 360°

90° + 90° +  BAD + ∠BCD = 360°

Thus we get

∠BAD + ∠BCD = 180°

Substituting the values from (1),

106° + ∠BCD = 180°

By further calculation

∠BCD = 180° - 106°

So we get

∠BCD = 74°

Therefore, the measure of angle BCD is 74°.

Angle BCD is a circumscribed angle of circle A. What is the measure of angle BCD?

Summary:

Angle BCD is a circumscribed angle of circle A. The measure of angle BCD is 74°.