"Question 10 If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lie on the third side.
Class 9 - Math - Circles Page 186"
Answers
A diameter of a circle divides the circle into 2 equal parts each of these two equal parts is called a semicircle.
Angle in a semicircle is a right angle.
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Given,
Two circles are drawn with sides AB and AC of the triangle ΔABC as diameters. Both these circles intersect each other at D.
To Prove:
D lies on BC
Construction: Join AD
To prove:
Since,AC and AB are the diameters of the two circles.
∠ADB =90°......(i)
∠ADC = 90°......(ii)
(Angle in the semi circle)
On adding eq i & ii
∠ADB + ∠ADC = 180°
∠BDC= 180°
Hence,BDC is straight line.
So , point of intersection D lies on the third side.
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Hope this will help you....
Answer:
Step-by-step explanation:
