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A circle is inscribed in an equilateral triangle. Smaller circles touch it and the sides of the triangle, the process continuing indefinitely. What is the sum of the areas of all the circles?

### Golden Thoughts

Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

# Weekly Challenge 32: Medicine Half Life

##### Stage: 4 and 5 Challenge Level:

A certain medicine is broken down by the body so that half of the remaining dose in the system is broken down every 12 hours.

If I regularly take 400mg of medicine in the morning and 400mg of medicine in the evening what is the long term effective level in my system after I take each tablet?

Extension: What will be the long term stable level after I take each tablet if the body breaks down half of the remaining dose every 6 hours?

Did you know ... ?

The 'half-life' of medicines is an important concept in medicine, particularly in the area of anti-depressants which take some time to reach active levels in the body.