﻿ Let ABCD be a quadrilateral with area 18, with side AB parallel to CD and AB = 2CD. Let AD be perpendicular to AB and CD. If a circle is drawn inside the quadrilateral ABCD touching all the sides, then its radius is : Kaysons Education

# Let ABCD be A Quadrilateral With Area 18, With Side AB parallel To CD and AB = 2CD. Let AD be Perpendicular To AB and CD. If A Circle Is Drawn Inside The Quadrilateral ABCD touching All The Sides, Then Its Radius Is

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## Question

### Solution

Correct option is

2

Let A (0, 0), B (2a, 0), C (a, 2r), D (0, 2r). Since the circle touches the parallel sides AB and CD its diameter is 2r so that the radius of the circle is r. Since it touches AD, distance of the centre from AB and AD is r and the coordinates of the centre are (rr).

or         2rx + ay – 4ar = 0

As the circle touches BC, distance of the centre from BC is also r.

From (1) and (2) we get a = 3, r = 2

So the required radius is 2.

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