For the triangle shown, where A, B and C are all points on

enigma123 · **Posted:** Sun Feb 05, 2012 5:33 pm


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For the triangle shown, where A, B and C are all points on a circle, and line segment AB has length 18, what is the area of triangle ABC?

(1) Angle ABC measures 30°.
(2)The circumference of the circle is 18 pi.

How come Statement 1 is not sufficient? Please help.

[Reveal] Spoiler: OA

C

dentobizz · **Posted:** Sun Feb 05, 2012 5:46 pm

Statement 1 is insufficient because--We are NOT given that the line segment AB=18 is the diameter of the circle,Hence we CANNOT assume that angle ACB is 90 (ONLY if the hypotenuse is the diameter then the angle opposite to it can be 90) and thus the 30-60-90 formula cannot be applied here using statement 1 alone.

by using statement 2 we can find the radius =9 ( C=2*pi*r=18 pi; r=9) , diameter = 18 , making AB the diameter (AB is given as 18) and thus angle ACB can be taken as 90 and using the info in statement 1 we can apply the 30-60-90 formula; get values of AC and BC and solve for the area of triangle ACB ( 0.5* AC *BC) .Answer C.

Hope it is clear now.

enigma123 · **Posted:** Sun Feb 05, 2012 6:12 pm

But again the same question - in the question no where it says that line AB passes through the centre of the circle so how can we take it as a diameter?

dentobizz · **Posted:** Sun Feb 05, 2012 6:26 pm

enigma123 wrote:

But again the same question - in the question no where it says that line AB passes through the centre of the circle so how can we take it as a diameter?

The diameter is the longest chord/line segment of the circle and all lines passing through the center of the circle and touching the circumference will be the diameters-- that is, they will have the same length,
hence in this question too when we find that AB=18 then we NOW KNOW that it IS the diameter of the circle [NO other line can have a length greater than 18 , and all line less than 18 will not be diameters]

So we are NOT assuming AB to be the diameter, rather when we calculate that diameter =18 (from st.2 )and we are already given AB=18 (question stem) ,then we just put these 2 pieces of information together, to get AB=18=Diameter. Hope this helps.

enigma123 · **Posted:** Sun Feb 05, 2012 6:34 pm

Thanks dento for a thorough explanation.

dentobizz · **Posted:** Mon Feb 06, 2012 2:13 pm

ur welcome, hope I got the point across

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For the triangle shown, where A, B and C are all points on

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