two circles are drawn with sides ab and ac of a triangle abc as diameters. circle intersect at d. if ab is 5, bd is 3 and ac is 6 find bc
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Step-by-step explanation:
Let us suppose that there are two circles having diameter AB and AC. The circles intersect at point D.
From the figure, ABC is a triangle.
Now we have to show that D lies on the line BC.
Join A and D as shown in the figure.
Given AB and AC are the diameter of the of the circle.
∠ADB = 90 .........1 (angles in a semi circle)
and ∠ADC = 90 ........2 (angles in a semi circle)
Add equation 1 and 2, we get
∠ADB + ∠ADC = 90 + 90
=> ∠ADB + ∠ADC = 180
So BDC is a straight line.
Hense D lies on BC.
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hope it help u
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