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08 Aug 2010, 19:48
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Tried to turn the left half of the triangle to a right triangle and determine the radius, which would be the hypotnuse. Then work on the other triangle. Not sure if I had the wrong idea or just a miscalculation.
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08 Aug 2010, 20:13
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Angle POQ = 90 degree.
Drop a perpendicular from P to the X axis to form a right angle triangle. Let the point where the perpendicular meets the X axis be D.
The length of the perpendicular is 1 unit and the base of the triangle is \(|-\sqrt{3}|\). The radius or the hypotenuse of the right angled triangle is 2 units.
With this information, we know that angle PDO = 90 degree, angle POD = 30 degree and angle DPO = 60 degree (ignore this).
Also from the diagram we know that angle POQ = 90 degree. Hence angle formed between POYaxis is 60 degree and angle between YaxisOQ is 30 degree.
Similarly drop a perpendicular from point Q to X axis, let the perpendicular touch the X axis at C.
Now angle QOC is 60 degree, angle QCO is 90 degree and angle OQC is 30 degree. Since PO = QO = radius of the circle hence QO = 2 units = hypotenuse.
Within the right angle triangle QOS, hypotenuse is 2 units, hence QC should be \(\sqrt{3}\) unit and OC should be 1 unit.
Answer: 1 unit -- Option B.
Drop a perpendicular from P to the X axis to form a right angle triangle. Let the point where the perpendicular meets the X axis be D.
The length of the perpendicular is 1 unit and the base of the triangle is \(|-\sqrt{3}|\). The radius or the hypotenuse of the right angled triangle is 2 units.
With this information, we know that angle PDO = 90 degree, angle POD = 30 degree and angle DPO = 60 degree (ignore this).
Also from the diagram we know that angle POQ = 90 degree. Hence angle formed between POYaxis is 60 degree and angle between YaxisOQ is 30 degree.
Similarly drop a perpendicular from point Q to X axis, let the perpendicular touch the X axis at C.
Now angle QOC is 60 degree, angle QCO is 90 degree and angle OQC is 30 degree. Since PO = QO = radius of the circle hence QO = 2 units = hypotenuse.
Within the right angle triangle QOS, hypotenuse is 2 units, hence QC should be \(\sqrt{3}\) unit and OC should be 1 unit.
Answer: 1 unit -- Option B.
