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9. Construct a Triangle Given the Length of Its Base, the Difference of the Base Angles and the Sum of the Other Two Sides

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This Demonstration shows a construction of a triangle given the length of the base , the sum of the other two sides and , and the difference of the base angles.

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Construction

Draw a line segment of length .

Step 1: Draw a circle with center so that the central angle . Measure out the point on at distance from .

Step 2: Let the point be the intersection of the perpendicular bisector of and .

Verification

Let , and .

Since by construction, . On the other hand, , so . Since is isosceles, . By construction, .

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Contributed by: Izidor Hafner (August 2017)
Open content licensed under CC BY-NC-SA

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