There are 8 line segments of lengths(in cm) 1,2,3,4,5,6,7,8.How many quadrilaterals can be made with these line segments if circles can be inscribed in the quadrilaterals made?

beatricalwu

beatricalwu

Answered question

2022-07-20

There are 8 line segments of lengths(in cm) 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8.How many quadrilaterals can be made with these line segments if circles can be inscribed in the quadrilaterals made?

Answer & Explanation

agyalapi60

agyalapi60

Beginner2022-07-21Added 17 answers

There is a much stronger necessary (and in fact sufficient) condition than the triangle inequality:
It is a well-known fact that a quadrilateral with sides a , b , c , d has an incircle iff a + c = b + d. Can you think of the reason for this?
So you have to count the number of quadruples { a , b , c , d } { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 } satisfying a + c = b + d.

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