If a circle is inscribed in a quadrilateral, what is the relationship between th
Practice Questions
Q1
If a circle is inscribed in a quadrilateral, what is the relationship between the lengths of the sides?
Opposite sides are equal
Sum of opposite sides is equal
All sides are equal
Adjacent sides are equal
Questions & Step-by-Step Solutions
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.
