Find the side AD of the quadrilateral ABCD, if AB = 3, BC = 4, CD = 5 and it is known that a circle can be inscribed in the quadrilateral ABCD.
From the condition, we know that we are given a quadrilateral ABCD, and the length of its three sides AB = 3, BC = 4, CD = 5 is also known. And we also know that a circle can be inscribed in the quadrilateral ABCD.
We need to find the fourth side of the quadrilateral AD.
For this we apply the following property of a quadrangle – a circle can be inscribed in a quadrilateral if the sums of its opposite sides are equal to each other.
That is, we write down the equality AB + CD = BC + AD.
Let’s compose and solve the equation:
3 + 5 = 4 + x;
x = 4.
Answer: AD = 4.
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