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Home Q & A Board Science-Related Homework Help Mathematics
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victoria1 victoria1
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7 years ago
This problem is from Copernicus�s De revolutionibus. Given the three sides of an isosceles triangle, to find the angles. Circumscribe a circle around the triangle and draw another circle with center A and radius AD=1/2 AB . Then show that each of the equal sides is to the base as the radius is to the chord subtending the vertex angle. All three angles are then determined. Perform the calculations with AB=AC=10 and BC=6.
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7 years ago
....ABC IS ISOCELLES TRIANGLE ..................... AB=AC............................. D IS MID POINT OF AB ....AD=DB..... THE CIRCLE WITH A AS CENTER AND RADIUS = AD=DB..... IT CUTS AC AT E ....... AE=AD=AB/2=AC/2...... DE IS THE CHORD OF THE CIRCLE ... TO PROVE .. AB / BC = AC / BC = AD / DE. PROOF.. IN TRIANGLES ABC AND ADE ANGLE BAC = ANGLE DAE.........COMMON ANGLE ................ AD/AB = 1/2 = AE/AC ..SINCE D AND E ARE MID POINTS OF AB AND AC ... HENCE THE 2 TRIANGLES ARE SIMILAR .... SO WE GET AD/AB = DE/BC = AE/AC AD*BC = AB*DE AD/DE = AB / BC .....SIMILARLY AB / BC = AC / BC = AD / DE.......PROVED ............. AB=AC=10......BC=6...... WE GET ...AD=AE=5 .......DE=BC/2 = 3 ......ANSWER ...
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bio_manbio_man
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