# In a trapezium ABCD , side BC is parallel to AD.Also the lengths of side AB,BC,CD and AD are 8,2,8 and 10 units respectively.Find the radius of the circle that passes through all four points A,B,C and D?

##### 1 Answer

#### Explanation:

The following is a figure for the question. So the whole thing looks like this one below.

Lets make some construction

Rest things are mentioned in figure.

Now applying pythagorean theorem

We get

Before proceeding any further i would like to tell that i'll find circumcentre of

Since it is a isoceles trapezium

Now , here's a relation

**Using cosine rule #AC=2sqrt21#**

Now again using that relation

Hope that helps.