If a circle is inscribed in a quadrilateral, what is the relationship between th

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Question: If a circle is inscribed in a quadrilateral, what is the relationship between the lengths of the sides?

Options:

Correct Answer: Sum of opposite sides is equal

Solution:

For a quadrilateral to have an inscribed circle, the sum of the lengths of opposite sides must be equal.

If a circle is inscribed in a quadrilateral, what is the relationship between the lengths of the sides?

If a circle is inscribed in a quadrilateral, what is the relationship between the lengths of the sides?

Step 1: Understand what an inscribed circle is. It is a circle that fits perfectly inside a shape, touching all sides.
Step 2: Know that a quadrilateral is a shape with four sides.
Step 3: For a circle to be inscribed in a quadrilateral, the lengths of the sides must have a special relationship.
Step 4: This relationship is that the sum of the lengths of one pair of opposite sides must equal the sum of the lengths of the other pair of opposite sides.
Step 5: If we label the sides of the quadrilateral as A, B, C, and D, then the condition can be written as: A + C = B + D.

Inscribed Circle in Quadrilaterals – A quadrilateral can have an inscribed circle (also known as a tangential quadrilateral) if and only if the sum of the lengths of its opposite sides is equal.