Q18 of 141 Page 438

is an isosceles triangle in which If and are midpoints of and respectively, prove that the points are concyclic.

Given, ABC is an isosceles triangle in which AB = AC. D and E are midpoints of AB and AC respectively.


∴ DE || BC


⇒ ∠ADE = ∠ABC ______________ (i)


AB = AC


⇒ ∠ABC = ∠ACB ______________ (ii)


Now,


∠ADE + ∠EDB = 180°[Because ADB is a straight line]


⇒ ∠ACB + ∠EDB = 180°


The opposite angles are supplementary.


∴ D, B, C, E are concyclic.


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