Question

Construct a triangle in which AB = 4 cm, ∠CAB = ${45}^0$ and BC = 4 cm. Draw a circle circumscribing the triangle ABC. The radius of the circle is:

• A. 2.82 cm
• B. 3 cm
• C. 4.5 cm
• D. 5.65 cm

Answer 1

The correct option is A 2.82 cm

Given AB = 4 cm, ∠CAB = ${45}^0$ and BC =4 cm.
So, the triangle is isosceles ∠ACB= ∠CAB = ${45}^0$
Therefore the given triangle is isosceles right angle triangle and AC is the hypotenuse.



So, $AC=\sqrt{4^2+4^2}=4\sqrt{2}=5.65$

Radius of the circumcircle of a right angled triangle is half the length of the hypotenuse.

So, $r=\frac{5.65}{2}=2.82$