Math CentralQuandaries & Queries


Question from Nazrul, a teacher:

The base, the difference of the angles adjoining the base and the sum of the other
two sides are given. How can I draw the triangle?
Please help me.

Always in construction problems you should work backwards: start with the completed figure, then see where the given elements fit in. So start with triangle ABC and extend the side BA beyond A to a point C' for which AC' = AC. (That is, BC' = b+c.) Then look closely at the resulting isosceles triangle ACC' with equal angles A/2 at C and C'. It remains only to notice how the angle C+(A/2) is related to B-C. (Hint: multiply C + (A/2) by 2 and subtract from 180 degrees.)


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