The green circle is the largest of the 3 circles. The red circle is the smallest circle and is located at the centre of the green circle. The yellow circle is the medium sized circle that touches the circumference of the small red circle and touches the circumference of the large green circle. Knowing that both the small red circle and the medium yellow circle are smaller than the large green circle and are placed within the large circle. The centre of the large green circle is O. The smallest circle has centre O and radius 2x centimetres.
The large circle has centre O and radius 2y centimetres. The third circle touches both the other two circles s shown. The three regions formed are coloured red, yellow and green as shown.
Q1) Explain fully why the radius of the third circle is (x + y) centimetres.
Write down, in terms of ㅠ, x and y, expressions for the area of the region that is coloured Q2) yellow,
Q3) green.
The area of the green region is twice the area of the yellow region.
Q4) Use this information to write down an equation involving x and y, and show that it simplifies to y^2 – 6xy + 5x^2 = 0.
Q5) Calculate the fraction of the design that is coloured yellow.
2007-09-28
16:50:39
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4 answers
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asked by
Anonymous