22 Feb 2013

Prize Maths Quiz: Five Circles in a Triangle (PMQ7)

Five Circles in a Triangle

To end a week of geometry problems, it is no surprise that PMQ7 is also a geometric puzzle.

The diagram shows five circles, each with integer radius, all touching the base of the large triangle. The four smaller circles all touch their two neighbouring circles, with the large circle touching all four. The two sides of the triangle each touch two of the circles.

Let the radii of the circles be a, b and c, such that a > b > c.

Given that c has a length of 4 units, find the area of the large triangle. You may leave it as an exact solution.

As always, I would like to see a method. As an interim solution, find the radii of all three circles.

Good luck!

How to Enter

Send your complete solution by email to [competition closed - email removed]. This email address shall be removed after the competition closes to avoid spam. This PMQ7 competition closes on Sunday 24 February at 23:59 GMT.

The Prize

The prizes for this PMQ7 are 3 free places in our Online Classroom for 2 months. The very first correct solution will receive a prize plus two others randomly selected from all the other correct answers. The email time stamp shall determine the order of entries received.
Quick Rules

Look at the expanded rules on our PMQ page.
Anybody can enter our Prize Maths Quiz; adults and students.
Use the official server clock in the right column to avoid late entries.
All emails and email addresses sent to us will be deleted after the winners have been processed.
DO NOT submit your entries to the comments section at the bottom of this post.
You CAN discuss it there but you must email us to enter the competition.
We adhere to COPPA guidelines regarding children's online safety and security.
Enjoy the challenge!
Send us your solution! You can't win if you don't participate.
Then tell your friends!

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