In a $Δ$ 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 $Δ$ ABC.

1 : 2

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1 : 1

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2 : 3

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1 : 3

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Solution

The correct option is A 1 : 2
AD = BD = 10

ABC is isosceles triangle. Median is same as perpendicular bisector. So $∠$ AFC = $∠$ AFB = 90 $^{\circ}$

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

So $∠$ ADF and $∠$ AEF = 90 $^{\circ}$ .
So, ADEF is a square.

Area of quadrilateral ADEF = 100

Area of triangle ABC = 200

So the required ratio is 1:2.

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In a ΔABC, 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 ΔABC.

In a $Δ$ 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 $Δ$ ABC.