Question #100384
Triangle ABC is inscribed in a circle. A median AM is drawn so that it intersects
the circle at point D. It is known that AB=1 and BD=1. Find BC.
1
Expert's answer
2019-12-18T12:06:36-0500

1.Since the triangle is inscribed in a circle, its median is the midpoint perpendicular. AOB=90°∠AOB = 90°

2. As AOAO is a common side of ΔAOCΔAOC and ΔAOBΔAOB, CO=OBCO=OB and AOC=A0B=90°∠AOC=∠A0B=90°, so AC=AB=1AC=AB=1.

3 As we see, ACDBACDB is inscribed in a circle and it's diagonals intersect at right angles, all sides (AC,CD,DB,AB)(AC,CD,DB,AB) are the same, so ABCDABCD is a square whose diagonal is equal 2\sqrt{2}


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