Where is my mistake ?
https://prikachi.com/images.php?images/592/7514592m.jpg
Here is what I did. From the given information we can deduce that QRS is a right triangle that is isoscales . Therefore if we put H in the middle of QS = > QH=HS = 1/2r= 0,5. Since the triangle is inscribed in the circle , QRS must measure 90 degrees and therefore QR/Qh = 1/square root of 2. From then on we easily find the area of the triangle QRS which should equal 1.h and find h. However, the number for h I find is not in the answers. What did I do wrong ?
p.s. Don`t mind my low score.. I was a noob back then a month ago when I started doing GMAT lol.
Triangle , rectangle , circle.
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Here's a visual. The dot in the middle is the center of the circle.
I'm assuming that the rectangle is conveniently inscribed so that the center of the circle is the center of the rectangle. Given that assumption, we know that the distance from the center to the midpoint of the length is HALF of the width, or (h/2).
Since the radius is 1, we know that the remaining distance is (1 - h/2).
From there we just use the fact that the areas are equal to find h.
The flaw (if I'm reading you correctly) in your solution is that you assumed the isosceles triangle is a 45-45-90, but that need not be the case. (Similarly, the length of the rectangle doesn't have to bisect the radius.)
I'm assuming that the rectangle is conveniently inscribed so that the center of the circle is the center of the rectangle. Given that assumption, we know that the distance from the center to the midpoint of the length is HALF of the width, or (h/2).
Since the radius is 1, we know that the remaining distance is (1 - h/2).
From there we just use the fact that the areas are equal to find h.
The flaw (if I'm reading you correctly) in your solution is that you assumed the isosceles triangle is a 45-45-90, but that need not be the case. (Similarly, the length of the rectangle doesn't have to bisect the radius.)
- BestGMATEliza
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Matt makes a great point! A triangle that is inscribed in a circle is a right triangle IF one of the sides of the triangle is the diameter of the circle. However, since this is not the case here, you cannot assume that it is a right triangle.
Eliza Chute
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Answer: Option B
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