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 circle.

Front

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

Back

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

Front

If one angle of a cyclic quadrilateral is 70°, what is the measure of the opposite angle?

Back

The opposite angle measures 110°.

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 are equal.

Front

If two angles of a cyclic quadrilateral are 60° and 120°, what are the measures of the other two angles?

Back

The other two angles are 120° and 60°.

Front

What is the angle at the center of a circle compared to the angle at the circumference subtended by the same arc?

Back

The angle at the center is twice the angle at the circumference.

Front

In a circle, if angle AOB = 80°, what is the angle subtended at point C on the circumference?

Back

The angle ACB is 40°.

Front

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

Back

The area can be calculated using Brahmagupta's formula: Area = √((s-a)(s-b)(s-c)(s-d)), where s is the semi-perimeter.

Front

What is the semi-perimeter of a cyclic quadrilateral?

Back

The semi-perimeter (s) is half the sum of the lengths of all sides: s = (a + b + c + d) / 2.

Front

If angles A and B are angles in a cyclic quadrilateral, what is the relationship between them?

Back

Angles A and B are supplementary, meaning A + B = 180°.