chetan2u wrote:
Attachment:
CIRCLE1.png
A, B, C and D are points on the circumference of circle with center at O. AC is the diameter of the circle and OD is parallel to BC. If the area of the sector formed by radius OD and OC, shown by blue colour, is \(\frac{1}{6}\)th of area of circle, what is the measure of line DE?
(A) \(\sqrt{3}\)
(B) \(\sqrt{2}\)
(C) 1
(D) \(\frac{\sqrt{3}}{2}\)
(E) \(\frac{1}{2}\)
New question
self made
OA: D\(\angle COD = 60^{\circ}\) as colored sector area is \(\frac{1}{6}\) of total circle's area
\(\angle COD = \angle BCA = 60^{\circ}\) (Alternate Opposite angles, \(BC||OD\))
Both \(\triangle ACB\) and \(\triangle DOE\) are \(30^{\circ}-60^{\circ}-90^{\circ} \triangle\)
In \(\triangle ACB\), Ratio of sides \(BC:AB:AC\) is \(1:\sqrt{3}:2\).
As\(BC =1\), then \(AC\) would be\(2\).
\(AC = 2 OD\)(Radius of circle), \(OD = \frac{AC}{2} =\frac{2}{2} =1\)
In \(\triangle DOE\),Ratio of sides \(OE:ED:OD\) is \(1:\sqrt{3}:2\).
As \(OD =1\), \(ED\) would be \(\frac{\sqrt{3}}{2}\)