Cyclic Quadrilaterals

Front

What is a cyclic quadrilateral?

Back

A cyclic quadrilateral is a four-sided figure (quadrilateral) where all vertices lie on the circumference of a single circle.

Front

What is the property of opposite angles in a cyclic quadrilateral?

Back

The sum of the opposite angles in a cyclic quadrilateral is 180°.

Front

If two angles of a cyclic quadrilateral are known, how can you find the other two angles?

Back

You can find the other two angles by subtracting the sum of the known angles from 180°.

Tags

CCSS.HSG.C.A.2

Front

What is the relationship between the angles subtended by the same arc in a circle?

Back

The angles subtended by the same arc at the circumference of the circle are equal.

Tags

CCSS.HSG.C.A.2

Front

How can you determine if a quadrilateral is cyclic using its angles?

Back

If the sum of a pair of opposite angles is 180°, then the quadrilateral is cyclic.

Front

What is the significance of the inscribed angle theorem in cyclic quadrilaterals?

Back

The inscribed angle theorem states that an angle inscribed in a circle is half the measure of the central angle that subtends the same arc.

Tags

CCSS.HSG.C.A.2

Front

Can a quadrilateral be cyclic if one of its angles is greater than 180°?

Back

No, a quadrilateral cannot be cyclic if any of its angles is greater than 180°.

Tags

CCSS.2.G.A.1

Front

What is the formula for the area of a cyclic quadrilateral?

Back

The area of a cyclic quadrilateral can be calculated using Brahmagupta's formula: Area = √((s-a)(s-b)(s-c)(s-d)), where s is the semiperimeter and a, b, c, d are the lengths of the sides.

Front

What is the semiperimeter of a quadrilateral?

Back

The semiperimeter of a quadrilateral is half the sum of the lengths of its sides.

Tags

CCSS.3.MD.D.8

Front

How do you prove that a quadrilateral is cyclic using its diagonals?

Back

A quadrilateral is cyclic if the product of the lengths of its diagonals is equal to the sum of the products of the lengths of its opposite sides.