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Geometry help?
What is the length of BC in the following picture if OA is 9 and the measure of arc AXC is 270 degrees?
1 Answer
- ?Lv 74 years ago
Assuming O is the center of the circle,
angle AOC measures
360° - 270° = 90°
and since OB extended to the circle is a radius perpendicular to chord AC,
it bisects both chord AC and angle AOC.
So angle AOB measures 90°/2 = 45°
and triangle AOB is a right isosceles triangle.
The hypotenuse, OA, therefore measures
√2 times side AB,
and side AB measures the same as BC.
So
(√2) BC = OA = 9 and
BC = 9/√2 = (9√2)/2 = 4.5 √2
= about 6.364
