Question

ABCD is a square. With centres B and C and radius equal to the sides of the squares, circles are drawn to cut one another at E inside square. Then angle BDE is equal to

Answer 1

Given : ABCD is a square. With centres B and C and radius equal to the sides of the squares, circles are drawn to cut one another at E inside square

To find : angle BDE

Solution:

Let say side of square = Radius = a

Then BC = BE = CE  = a

Equilateral triangle

=> ∠BCE = 60°

=>  ∠BCD = 90°  ( angle of square)

=> ∠ECD = 90° - 60° = 30°

now CE = CD  = a

=> ΔECD is an isosceles triangle

∠CDE =  ∠CED

∠CDE + ∠CED + ∠ECD = 180°

=> 2∠CDE  + 30° = 180°

=>  ∠CDE = 75°

∠CDB = 45°   ( as BD is diagonal)

=> ∠BDE = ∠CDE  - ∠CDB

=>  ∠BDE = 75° - 45°

=> ∠BDE = 30°  

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