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Considering the above diagram, the following relation holds true.
m∠ADB=180∘−m∠ACB
By definition, a circumscribed angle is an angle whose sides are tangents to a circle. Since ∠ADB is a circumscribed angle, DA and DB are tangents to ⊙C at points A and B, respectively. By the Tangent to Circle Theorem, CA is perpendicular to DA and CB is perpendicular to DB.
m∠DAC=90∘, m∠CBD=90∘