Two semicircles and two right triangles. What fraction of the large triangle does the small one cover?
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Solution
The fraction is 2/9.
First we draw two chords from the small triangle vertices to the semicircle touch point. From Thales we know that they are at right angles with the other chords as shown.
From the 1 : 2 proportion of the semicircles we infer the lengths as shown. Now the little triangle has area ab, whereas the large one has 9ab/2. The fraction follows.
Poem
Perseverence Rover landed on the Red Planet
The Sky Crane helped to touch
Her softly
The Queen of the stars is in love
The icy lady is cold outside
But her heart is like a volcano
The Red Planet waited for Perseverence since years
A fabulous moment,
The Martians are happy !!!
