Question 112
Fach of the circles of equal radii with centres A and B pass through the centre of one another circle they cut at C and D then ∠DBC is equal to
Solution
Since the circles pass through the centre of each other, the distance between their centres will be equal to the radius of the circle. Distance between the midpoint of line joining centres and centres = r/2.
Connecting the points of intersection and midpoint of the radii, we get a right angled triangle.
Cos A = (r/2)/(r) = 1/2
=> A = 60 degrees.
∠DBC = 2* angle A = 2*60 = 120 degrees.
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