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# Paul has a circular garden in his backyard. He puts poles

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Paul has a circular garden in his backyard. He puts poles [#permalink]  20 Jul 2006, 10:29
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Paul has a circular garden in his backyard. He puts poles A,B and C on the circumference of his garden. Then he ties ropes between these poles. Is length of one of the ropes is equal to the diameter of his garden?

1. Slope of line joining pole A and B is 3/4 and slope of line joining poles B and C is -4/3
2. Length of line joining pole A and B is 12 and length of line joining B and C is 5.
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Note that the product of slopes of two perpendicular lines is equal to -1 (and the slopes of two parallel lines are equal). Note also that the angle in a semicircle is 90 degrees.

Statement 1: product of slopes = -1, hence, AB is perpendicular to BC and B is a right angle. Which means AC is a diameter such that ABC form a semi-circle.

Statement 2: I am not sure about this part. AB = 12 and BC = 5 does not necessirily mean AC = 13 (implying a right triangle). Hence, I am not sure whether statement 2 alone is sufficient.

I will go with Answer A. I might have to think about statement 2 again to be sure.

-mathguru.
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Lots of triangles that have two sides of length 5 and 12 can be drawn- they need not be right triangles, though if the third side is of length 13, t will be. Therefore, (2) is insufficient. The above reasoning for (1) is correct, so go with A!
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one more for (A).. same reasoning as above.
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OA is A

You guys are bang on target. Like kevin, I made this question myself.
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kevincan wrote:
Lots of triangles that have two sides of length 5 and 12 can be drawn- they need not be right triangles, though if the third side is of length 13, t will be. Therefore, (2) is insufficient. The above reasoning for (1) is correct, so go with A!

Try drawing a triange with two sides measuring 5 & 12, having its edges on the circle's circumference - the third side will always come out 13.
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xsports wrote:
kevincan wrote:
Lots of triangles that have two sides of length 5 and 12 can be drawn- they need not be right triangles, though if the third side is of length 13, t will be. Therefore, (2) is insufficient. The above reasoning for (1) is correct, so go with A!

Try drawing a triange with two sides measuring 5 & 12, having its edges on the circle's circumference - the third side will always come out 13.

Only if the the third side passes through the centre of the circle!
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It always will - impossible to draw the triangle otherwise.
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