# The Hardest Circle O-level Math Question Ever

Are you ready to take on the most challenging and hardest math questions the NECTA O-level Certificate has to offer? We’ve put together what we believe to be the hardest circle question given to O-level (Form 1 – Form 4) student.

Question 01: Cirlce Question : A and B are the centers of two circles which touch each other externally. Both circles touch a third circle, center C, internally. If AB = 13cm, BC = 14cm, CA = 11cm. Calculate the radii of the circles.

Why is this question so hard? If it’s the first time seeing question like this, it will take you more than half an hour to figure out what’s the correct arrangement of the three circles altogether. But once you find the correct arrangement, the question is done because the steps are very easy. See the following diagrams, and bet which one is the correct arrangement of the three circles:

The answer is B and from there;

x + y = AB
rArr x + y = 13
Also, x + 11 = y + 14 rArr x – y = 3
So now we have two equations:
{(x,+,y,=,13),(x,-,y,=,3):}
Then solve simultaneously to get the value of x and y
You get x = 8 and y = 5

Hence the radius of the circle with center C = y + 14 = 11 + x = 19 cm

Therefore, The radii of the circles with centers A, B and C are 8 cm, 5 cm, and 19 cm respectively.

## 4 thoughts on “The Hardest Circle O-level Math Question Ever”

1. Juan says:

From the diagrams, where are x and y? x + y = AB, where do you get those x and y? 🧐🧐🤨🧐🧐

1. Hans says:

I think x is the radius of the circle with centre A and y is the radius of the circle with centre B

1. Laban Mussa says:

probably

2. Laban Mussa says:

where’s x and y in your diagrams?