If in the following figure (not to the scale), ∠ACB = 135o and the radius of the circle is 2√(2) cm, then the length of the chord AB is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e 4 cm
| Understanding | Application |
| We will property of cyclic quadrilateral in which Sum of the opposite angle of cycle quadrilateral is 180o |
In quadrilateral ACBD, ∠ACB & ∠ADB are opposite so the sum would be 180o. ⇒ ∠ADB = 180 - 135 = 45o |
| The angle at the center of a circle is twice the angle at the circumference. |
Let the center of the circle be E then ⇒ ∠ACB = 2 × ∠ADB ⇒ ∠ACB = 90o In the right-angle triangle ABE AB2 = AE2 + BE2 AB = √{2(2√2)2} AB = 4cm |