In these lessons, we will learn

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More Geometry Lessons

### Cyclic Quadrilateral

### Properties of a Cyclic Quadrilateral

*ABC* = 90˚ ( angle of semicircle )

∠*ABD* + ∠*DBC* = ∠*ABC*

∠*ABD* + 36˚ = 90˚

∠*ABD* = 54˚

∠*ABD* + *x* = 180˚ ( interior opposite angles of a cyclic quadrilateral)

* x* = 180˚ – 54˚ = 126˚

This video shows how to use the properties of a cyclic quadrilateral to find missing angles.

A quadrilateral is cyclic when its four vertices lie on a circle.

Opposite angles in a cyclic quadrilateral adds up to 180˚.

This video shows how to use the properties of a cyclic quadrilateral to find missing angles. Opposite angles in a cyclic quadrilateral adds up to 180˚. Interior opposite angles are equal to their corresponding exterior angles.
Circle theorems - Alternate segment theorem and Cyclic quadrilaterals.

### Proof for the Cyclic Quadrilateral

This video shows how to prove that opposite angles in a cyclic quadrilateral are supplementary. It is based on the theorem: Angle at the center is twice angle at the circumference.
Circle Geometry: Cyclic Quadrilateral (What is the relationship between the angles of a quadrilateral that is inscribed in a circle?) This video shows how to prove that opposite angles in a cyclic quadrilateral are supplementary.

Arcs Between Parallel Lines

Using a computer model to show that the arcs between two parallel lines must be congruent.

You can use the free Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

- what is a cyclic quadrilateral.
- the properties of a cyclic quadrilateral
- the opposite angles of a cyclic quadrilateral are supplementary.
- the exterior angle of a cyclic quadrilateral is equal to the interior opposite angle.

- to prove that the opposite angles of a cyclic quadrilaterals are supplementary.

Related Topics:

More Geometry Lessons

A cyclic quadrilateral is a quadrilateral with 4 vertices on the circumference of a circle.

In the diagram shown below, *ABCD* is a cyclic quadrilateral because all its vertices lies on the circumference of the circle.

Property 1: In a cyclic quadrilateral, the opposite angles are supplementary i.e. they add up to 180˚.

* a* + *c* = 180 ˚**, ***b* + *d* = 180 ˚

* Example: *

*AC* is a diameter of the circle. Find the value of *x*.

* Solution: *

∠

∠

∠

∠

A quadrilateral is cyclic when its four vertices lie on a circle.

Opposite angles in a cyclic quadrilateral adds up to 180˚.

Property 2: The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle.

* Example: *

The exterior angle ∠* ADF* is equal to the corresponding interior angle ∠* ABC.
*The exterior angle ∠

* Example: *

Find the values of *x* and *y* in the following figure.

* Solution: *

* x* = 98˚ ( Corresponding opposite angles of a cyclic quadrilateral )

*y* + 27˚ = 53˚ (Corresponding opposite angles of a cyclic quadrilateral)

*y* = 26˚

Using a computer model to show that the arcs between two parallel lines must be congruent.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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