Q. 11 E4.5( 6 Votes )

# 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.

Answer :

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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