What is the perimeter of quadrangle ABCD in which a circle is inscribed?
1) AB+DC=8
2) BC=5
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diebeatsthegmat
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IMO E
1) AB + CD = 8
Dont know any of the four sides (Not Sufficient)
2) BC = 5
(Obviously not sufficient alone)
Together; you still dont know AD, AB and CD (although we know AB+CD) Not sufficient
1) AB + CD = 8
Dont know any of the four sides (Not Sufficient)
2) BC = 5
(Obviously not sufficient alone)
Together; you still dont know AD, AB and CD (although we know AB+CD) Not sufficient
diebeatsthegmat wrote:What is the perimeter of quadrangle ABCD in which a circle is inscribed?
1) AB+DC=8
2) BC=5
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Anurag@Gurome
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Let the points at which the circle touches AB, BC, CD, and DA of the quadrangle ABCD be P, Q, R, and S.
So, let AP = AS = x,
BP = BQ = y, CQ = CR = z, and DR = DS = w. (Tangents drawn from same point are equal in length)
So, perimeter of the quadrangle is 2x+2y+2z+2w.
Consider first (1) alone.
Now, AB + CD = x+y+z+w = 8.
So perimeter is 2*8 = 16
Or (1) alone is sufficient.
Now (2) alone is not sufficient.
The correct answer is (A).
So, let AP = AS = x,
BP = BQ = y, CQ = CR = z, and DR = DS = w. (Tangents drawn from same point are equal in length)
So, perimeter of the quadrangle is 2x+2y+2z+2w.
Consider first (1) alone.
Now, AB + CD = x+y+z+w = 8.
So perimeter is 2*8 = 16
Or (1) alone is sufficient.
Now (2) alone is not sufficient.
The correct answer is (A).
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