



 
Hi Caitlin, The circumference of a circle is 2r and your circle has a circumference of 6. Thus
and therefore r = 3. In the diagram C is the centre of the circle and M is the midpoint of PQ. The area of the inscribed circle is 3 time the area of triangle PQC.
The area of a triangle is half the base times the height and hence the area of triangle PQC is MQ MC. Since the circle has radius 3, QC = 3. Also the inscribed triangle is equilateral and thus each of its angles measures 60 degrees. Thus the measure of angle MQC is 30 degrees and angle CMQ is a right angle so the measure of angle QCM is 60 degrees. Can you now find the lengths MC and MQ? Penny  


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