Question

AB is a diameter of a circle, centre O. C is a point on the circumference of a

circle, such that ∠CAB = 2 × ∠CBA. Find ∠CBA.​

Answer 1

Step-by-step explanation:

ACB=90° (Angle subtended on semi-circle)

In, △ACB,

∠CAB=180°-(∠ACB+∠CBA)

=180°-(90°+70°)

=20°

Now,

∠DCA+∠ACB+∠BAC+∠DAC=180° [Sum of opp. anglesof cyclic quadrilateralis supplementary.]

∠DCA+90°+20°+30°=180°

∠ACD=180°-40°

∠ACD=40°

Hence, 40° is the correct answer.

Answer 2

Answer:

angle C=90(angle in a semicircle =90)

angle C+ angle CAB+ angle CBA =180(A.S)

90+2 angle CBA+ angle CBA =180(GN: angle CAB=2angle CBA)

3 angle CBA=90

angle CBA =30