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Show that the Circle Drawn on Any One of the Equal Sides of an Isosceles Triangle as Diameter Bisects the Base. - ICSE Class 10 - Mathematics

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Question

Show that the circle drawn on any one of the equal sides of an isosceles triangle as diameter bisects the base.

Solution

Join AD.
AB is the diameter.
∴ ∠ADB = 90º (Angle in a semi-circle)
But, ∠ADB + ∠ADC = 180º (linear pair)
⇒ ∠ADC = 90º
In ΔABD and ΔACD,
∠ADB = ∠ADC (each 90º)
AB = AC (Given)
AD = AD (Common)
ΔABD ≅ ΔACD (RHS congruence criterion)
⇒ BD = DC (C.P.C.T)
Hence, the circle bisects base BC at D.

 

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Solution Show that the Circle Drawn on Any One of the Equal Sides of an Isosceles Triangle as Diameter Bisects the Base. Concept: Tangent to a Circle.
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