﻿ Let ABCD be a quadrilateral with area 18, with side AB parallel to the side 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 The Side 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 CD = α so that AB = 2α be two parallel lines. Taking A as origin the co-ordinate are A (0, 0), B(2α, 0), D(0, 2r) and C(α, 2r). Since the circle is touching the axes of co-ordinates it is of form

The above line (2) is a tangent to circle (1). Apply the condition of tangency i.e., p = r we have

Area of quadrilateral  i.e. trapezium ABCD is

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