Question
AB is the diameter of a circle centered at O. A tangent
drawn at point C intersects the extension of AB at point D. If ∠CAB = 38°, find the value of ∠CDB.Solution
ATQ,
Angle made by the diameter of a circle on the arc of the circle is 90°, i.e. ∠ACB = 90°.
Sum of all angles in a triangle is 180°.
So, ∠CAB + ∠CBA + ∠ACB = 180°
Or, 38° + ∠CBA + 90° = 180°
Or, ∠CBA = 180° - 128°
Or, ∠CBA = 52°
Now, ∠CBA + ∠CDB = 180°
(Linear pair of angles)
So, ∠CDB = 180 - 52 = 128°
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