If in the following figure (not to the scale), ∠ACB = 135° and the radius of the circle is $2\sqrt{2}$ cm, then the length of the chord AB is:
Answer & explanation
Correct answer: option 3
We have,
Radius of the circle = 2√2 cm
∠ACB = 135
We know that,
The sum of the opposite angle of the cycle quadrilateral is 180.
The angle at the center of a circle = Twice the angle at the circumference
∠ACB + ∠ADB = 180o
= 135 + ∠ADB = 180o
= ∠ADB = 180 – 135 = 45o
We know that,
O is the center of the circle.
∠BOA = 2 ∠BDA
= ∠BOA = 2 × 45
= ∠BOA = 90o
We know that,
OA = OB = 2√2
According to the Pythagoras theorem,
AB2 = OB2 + OA2
= AB2 = (2√2)2 + (2√2)2
= AB2 = 8 + 8
= AB = √16
AB = 4