Question

In a triangle ABC, AB = AC = 20 cm. D, E, F are the midpoints of sides AB, AC and BC respectively. Find the ratio of area of quadrilateral ADFE to the area of triangle ABC .

• A. 1 : 2
• B. 1 : 1
• C. 2 : 3
• D. 1 : 3

Answer 1

The correct option is A 1 : 2

AD = BD = 10

ABC is isosceles triangle. Median is same as perpendicular bisector. So angle AFC = Angle AFB = 90

BC is tangent to the circle; AF is perpendicular so AF must be the diameter. (Radius is perpendicular to tangent)

So angle ADF and angle AEF = 90 degrees. Let DF = x.

Area ADF = Area AFE = $\frac{1}{2}$*10 * x = 5x, Area ADFE = 10x

Area ABF = Area AFC =$\frac{1}{2}$ * 20 * x = 10x, Area ABC = 20x

So the required ratio is 1:2