In this video, let's learn an interesting property about sightly Quadratus.
Now, first, let's try to understand what do we mean with this cyclic quadrilateral?
All right, over here I have a circle and I have a quadrilateral over here.
Now, you can see that all the vertices that is all these four pieces of the quadrilateral are on the
circle.
This type of a quadrilateral is called Acyclic Quadrilateral.
So over here, ABCDE is a cyclic quadrilateral already.
Now, in cycling quadrilaterals, the opposite angles are supplementary.
That is angle a plus angle.
See over here is equal to 180 degrees and in a similar manner.
Angle B plus angle D also is equal to 180 degrees.
Now this is an important property.
Let's quickly try to understand why the opposite angles in a cyclic quadrilateral are supplementary
SailPoint or is the center of the circle.
And this is that center.
Let me join B with Orb and let me join David or.
All right, now, let's take that this angle over here is to Alpha and let this over here be to Beta.
All right, now we know that angle B, C, D is the angle subtrend that by the arc beardie, right?
The minor arc beardie.
Therefore we can see that angle B, C, D, let me right that over here.
Angle BCT will be equal to half the measure of Arc B, right.
Which is equal to two alpha.
So ABCDE will be equal to two alpha divided by two which is equal to Alpha.
Similarly you can see that angle B 80, that's angle B 80 will be equal to off to beta.
Right.
So that's two beta divided by two which gives you beta.
Now over here you can see that two alpha plus two beta is making one complete revolution around the
center.
So two alpha plus two beta is equal to 360 degree.
Right.
Therefore, we can see that Alpha plus beta is 360 by two.
That's equal to 180 degrees.
That's why we say that in the case of a cyclic quadrilateral, the opposite angles are supplementary.