Question

Find the length of circumradius of a right-angled triangle whose adjacent sides are 3cm and 4cm?

• A. 2 cm
• B. 2.5 cm
• C. 3 cm
• D. 3.5 cm

Answer 1

The correct option is B

2.5 cm

As per the question we have to find out the length of circumradius of a right-angled triangle whose adjacent sides are 3cm and 4cm.

Let BAC be a triangle where AB = 3 cm and AC = 4cm.

We draw the perpendicular bisector of AB and BC as RS and PQ respectively.

AR = $\frac{3}{2}=1.5cm$

RO = $\frac{4}{2}=2cm$

The length of the circumradius is equal to AO.

By Pythagoras theorem

$A{O}^2=A{R}^2+R{O}^2$

On substituting the values we get:

$A{O}^2={1.5}^2+2^2$

$\Rightarrow AO=\sqrt{{1.5}^2+2^2}$

$\Rightarrow AO=2.5cm$

Hence, the circumradius of the triangle is 2.5 cm.