rahulvsd wrote:AB is the diameter of the circle. CD is parallel to AB. What is the length of minor arc CD?
(1) The radius of the circle is 12.
(2) The measure of ∠CAB is 30º.
OA: [/img]c[/img]. Can someone explain?
When the statements are combined:
When an inscribed angle (which is formed by 2 chords) and a central angle (which is formed by 2 radii) intercept the same arc, the inscribed angle = 1/2 the central angle.
Inscribed angle CAB and central angle COB both intercept arc BC.
Thus, COB = 60.
Since 60/360 = 1/6, the length of intercepted arc BC = 1/6 of the circumference.
Since CD is parallel to AB, inscribed angle DCA = 30.
Applying the same reasoning used above, we can determine that the length of arc AD = 1/6 of the circumference.
Since arc ADCB = 1/2 of the circumference, arc CD = 1/2 - 1/6 - 1/6 = 1/6 of the circumference.
Statement 1 indicates that r=12, implying that C = 24Ï€.
Thus, arc CD = (1/6)*24Ï€ = 4Ï€.
SUFFICIENT.
The correct answer is
C.
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