Triangle ABC is equilateral. D, the midpoint of BC, is the centre
of the semi-circle whose radius is R which touches AB and AC, as
well as a smaller circle with radius r which also touches AB and
AC. What is the value of r/R?
Stage: 4 Challenge Level:
The smaller of two similar rectangles has height $2$ units; the larger rectangle has length $6$ units.
If one rectangle has twice the area of the other, find the length of the smaller rectangle.
This problem is taken from Tony Gardiner's 'Extension Mathematics Gamma' book.
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