Q11 of 24 Page 296

ABC is an isosceles triangle in which ∠ABC = ∠ACB and Median AD = BC. If AB = √2 cm, let us write the length of circumradius of this triangle.

Given: Median AD = BC ….(1)


From (1) we can say it is a right angle triangle as well,



AB = √2 cm


AC = √2 cm (isosceles triangle)


In a right angle triangle,


(BC)2 = (AB)2 + (AC)2


⇒ (BC)2 = (√2)2 + (√2)2


⇒ (BC)2= 2 + 2


⇒ (BC)2= 4


⇒ BC = 2cm


As we know,


length of circumradius of a right angled triangle = 1/2 length of hypotenuse


⇒ AD = 1/2 BC


⇒ AD = 1/2 (2)


⇒ AD = 1cm


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