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Olympiad Mathematics Question 1

 

UK Junior Mathematical Olympiad 2015

Organised by The United Kingdom Mathematics Trust

Question :

Two circles of radius 1 cm fit exactly between two parallel lines, as shown in the diagram. The centres of the circles are 3 cm apart.

What is the area of the shaded region bounded by the circles and the lines?

math

 

 

 

 

 

 

Solution: (6−π)cm2

The area bounded by the circles can be calculated by subtracting the area of one circle from the area of the 3cm× 2cm rectangle with edges passing through the centres of the circle. Therefore the shaded area is (6−π)cm2.

 

 

Source:

Questions and Solutions 2015

https://www.ukmt.org.uk/pdfs/jmo15Q&S.pdf

Filed under: Olympiad Mathematics Question bank on March 23rd, 2016

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