AB is the diameter of a circle with centre O. C and D are two points on the circumference of the circle on either side of AB, such that ∠ CAB = 42° and ∠ ABD = 57°. What is difference ( in degrees) between the measures of ∠ CAD and ∠ CBD ?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 75 and 105
Solution :
Given : C and D are the points on the circumference of the circle
∠CAB = 42° and ∠ ABD = 57°
Concept used : The angle suntended by the diameter to the circumference of the circle is a right angle , i.e. ∠ACB = ∠ADB = 90°
Now,
From the figure,
In △ACB,
∠ACB + ∠ABC + ∠BAC = 180°
90° + 57° + ∠BAC = 180°
∠BAC = 33°
Also in △ADB,
∠ADB + ∠ABD + ∠BAD = 180°
90° + 42° + ∠ABD = 180°
∠ABD = 48°
Now require measurements are ∠CAD and ∠CBD.
Therefore, ∠CAD = ∠BAC + ∠BAD = 33° + 42° = 75°
Similarly, ∠CBD = ∠ABD + ∠ABC = 48° + 57° = 105°
Hence ∠CAD = 75° and ∠CBD = 105°.