Two congruent triangles ABC and DEF are inscribed in two semicircles. What is the area of both the circles?
(1) Perimeter of one of the circles if 10 units
(2) BC=8 units and DF=6 units.
Don't have an OA. But I'm certain the answer is A
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Geometry Problem
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Anurag@Gurome
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Statement 1: We don't have any information about the other circle.knight247 wrote:Two congruent triangles ABC and DEF are inscribed in two semicircles. What is the area of both the circles?
(1) Perimeter of one of the circles if 10 units
(2) BC=8 units and DF=6 units.
Not Sufficient
Statement 2: BC = 8 and DF = 6 implies EF = 8 and AC = 6 as the triangles are congruent. But we don't have any necessary information to determine the area of the circle.
Not Sufficient
1 & 2 Together: Doesn't yield any new or necessary information.
Not sufficient.
The correct answer is E.
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amit2k9
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a 2r+pi*r = 10 where r = 10/5.414 approx = 1.7
nothing has been mentioned about the other circle. Not sufficient.
b ABC may or may not be right triangle.similar it is true for DEF too.
not sufficient.
a+b not sufficient.
E it is.
nothing has been mentioned about the other circle. Not sufficient.
b ABC may or may not be right triangle.similar it is true for DEF too.
not sufficient.
a+b not sufficient.
E it is.
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Then the statements will contradict each other and the question will never appear in actual GMAT or any legitimate material.BY wrote:If statement-1 replaced as : Perimeter of triangle ABC is 10 and the statement-2 is same, then what will be the answer ?
That's because from statement 2, BC = 8 and AC = 6.
Hence, perimeter of ABC will be always greater than 10.
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mirantdon
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+1 for A.
If the triangles are congruent then the information about the other semicircle is immaterial .
Since both the triangles will share the same base . hence the length of both these will be equal . And also any triangle within a semicircle will subtend 90 degrees . hence if the triangle are congruent we can consider this as a uniform circle
A : Statement A provides us a Circumference ,(Common base for congruent triangles) well thats enough isnt it ? SUFFICIENT
B We are not sure what side is congruent to which one
hENCE a
Kindly provide your inputs
If the triangles are congruent then the information about the other semicircle is immaterial .
Since both the triangles will share the same base . hence the length of both these will be equal . And also any triangle within a semicircle will subtend 90 degrees . hence if the triangle are congruent we can consider this as a uniform circle
A : Statement A provides us a Circumference ,(Common base for congruent triangles) well thats enough isnt it ? SUFFICIENT
B We are not sure what side is congruent to which one
hENCE a
Kindly provide your inputs
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rishijhawar
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mirantdon, the question doesn't mention that both semi-circle are part of the same circle (and thats why probably you assumed the triangles have same base). hope it helps.
