Question

the length of perpendicular sides of a right angle triangle are 7 cm and 24 cm respectively then find the radius of its circumcircle​

Answer 1

Answer:

The radius of the circumcircle is 12.5 cm

Step-by-step explanation:

Given as :

The circumcircle with center O is drawn over right angled triangle ABC

The measure of sides of triangle are

AB = a = 7 cm

AC = b =24 cm

The radius of circumcircle = r cm

Let The length of hypotenuse side = BC = c

∵ For right angled triangle

Hypotenuse² = perpendicular² + Base²

Or, BC² = AC² + AB²

Or, c² = b² + c²

Or, c² = (24)² + 7²

Or, c² = 576 + 49

Or, c² = 625

∴   c = √625

Or, c = 25 cm

So, The length of hypotenuse side = BC = c = 25 cm

Now,

Radius of circumcircle = $\dfrac{a b c}{\sqrt{(a + b + c) (a + b - c) (b + c - a) (c + a -b)} }$

Now putting the value of side a ,b ,c

r = $\frac{7\times 24\times 25}{\sqrt{(7+24+25)(7+24-25)(24+25-7)(25+7-24)}}$

Or, r = $\dfrac{4200}{\sqrt{112,896} }$

∴   r = $\dfrac{4200}{336}$

i.e r = 12.5 cm

So, the radius of the circumcircle = r = 12.5 cm

Hence, The radius of the circumcircle is 12.5 cm  . Answer