Question

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 :

• A. 112°
• B. 148°
• C. 132°
• D. 142°

Answer 1

The Correct Option is C

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°.