theaream of cyclic quadrilateral class 11 th math
Answers
Answer:
The definition states that a quadrilateral which is circumscribed in a circle is called a cyclic quadrilateral. It means that all the four vertices of quadrilateral lie in the circumference of the circle. Let us understand with a diagram.
In the figure given below, the quadrilateral ABCD is cyclic.
Cyclic Quadrilateral 1
Let us do an activity. Take a circle and choose any 4 points on the circumference of the circle. Join these points to form a quadrilateral. Now measure the angles formed at the vertices of the cyclic quadrilateral. It is noted that the sum of the angles formed at the vertices is always 360o and the sum of angles formed at the opposite vertices is always supplementary.
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Cyclic Quadrilateral Angles
The sum of the opposite angles of a cyclic quadrilateral is supplementary.
Let ∠A, ∠B, ∠C and ∠D are the four angles of an inscribed quadrilateral. Then,
∠A + ∠C = 180°
∠B + ∠D = 180°
Therefore, an inscribed quadrilateral also meets the angle sum property of a quadrilateral, according to which, the sum of all the angles equals 360 degrees. Hence,
∠A + ∠B + ∠C + ∠D= 360°
Radius of Cyclic Quadrilateral
If a, b, c and d are the successive sides of a cyclic quadrilateral, and s