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Quantitative Aptitude Question on Geometry

In the given figure, AB is the chord of the circle with centre ‘O’. A tangent AT is drawn at point ‘A’ so that angle BAT = 48°, then measure of angle ADB is :
AB is the chord of the circle with centre O

A

112°

B

148°

C

132°

D

142°

Answer

132°

Explanation

Solution

Circle with radius OA
OA = OB {radii}
And angle OAT = 90° {Since, AT is tangent}
And angle OAB = 90 - 48 = 42°
In triangle OAB;
Angle OAB = angle OBA {angles opposite to equal sides are equal}
So, angle AOB = 180 - 42 - 42 = 96°
So, angle AEB = 96/2 = 48° {Since, ‘O’ is the circum-centre}
Since, AEBD is a cyclic quadrilateral.
So, angle AEB + angle ADB = 180°
Or, angle ADB = 180 - 48 = 132°
So, the correct option is (C) : 132°.