In the circle pictured above, AB=2√5, CD=1, and AC is a diameter GMAT Problem Solving

The problem is simple now:

By Pythagoras theorem in triangle ABD, we have:
20 = AD² + BD²
20 = AD² + AD

So, solving the equation, we will get:

AD = – 5 and 4

But side cannot be negative, therefore AD = 4

This means, diameter = 5

Hence, circumference = 5π

Correct option: A

3 right triangles:

So, diameter = AC = x + 1 = 5

Circumference = 2πr = 5π

Correct option: A

AB is aright triangle with hypotenuse as 2√5

So, AB² = 20

In triangle ABD, AB² = AD² + BD²

Now if you look at the options the circumference is provided

2πr and AD = Diameter of circle – 1

Now if you have a look at options, in all options except the first one, AD when squared is returning a value larger than AB² which is not possible since AB is the hypotenuse of right triangle ABD.

So, we can eliminate all except A which is the answer

Correct option: A