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AB is the diameter of the circle and the points C and D are on the circumference such that $\angle CAD=30^o$. What is the measure of $\angle ACD$?

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In the given figure AB is the diameter of the circle

Angle CAD = 30 degree and Angle CBA = 70 degree

Angle ACD = ?

Drawing lines DB and AC in the figure

now Angle CAD = Angle CBD = 30 degree ( Since a chord of a circle subtends equal angles on all its circumference)

⇒ Angle DBA = 40 degree

now Angle DBA = Angle ACD = 40 degree ( Since a chord of a circle subtends equal angles on all its circumference)

Angle CAD = 30 degree and Angle CBA = 70 degree

Angle ACD = ?

Drawing lines DB and AC in the figure

now Angle CAD = Angle CBD = 30 degree ( Since a chord of a circle subtends equal angles on all its circumference)

⇒ Angle DBA = 40 degree

now Angle DBA = Angle ACD = 40 degree ( Since a chord of a circle subtends equal angles on all its circumference)

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