Question

ABC is a right angled triangle, right angled at B such that BC = 6 cm and AB = 8 cm. A circle with centre O is inscribed in ΔABC. The radius of the circle is
A. 1 cm
B. 2 cm
C. 3 cm
D. 4 cm

Answer 1

Answer:

2, using the formula of area 1/2 *b*h and herons formula of triangle

Answer 2

To find the radius of a circle inscribed in a right angled triangle, we can use the formula

r = (a + b – c) / 2

Explanation:

So, as per the information that has been given to us,  

The triangle is right angled at B.

Also, BC = 6cm and AB = 8cm.

Because it is a right angled triangle so, we can use the Pythagorean theorem to find the third side of the triangle.

We have AB^2 + BC^2 = AC^2.

Or, AC^2 = AB^2 + BC^2.

AC^2 = 8^2 + 6^2.

AC^2 = 64 + 36

AC^2 = 100.

Or, AC = √100

AC = 10 cm.

Now that we  have the third side of the triangle, so we can use the above mentioned formula to calculate the radius of the Circle.

Here we have r = (BC + AB – AC) / 2

 r = (6 +8 – 10) / 2

 r = (14 – 10) / 2

 r = 4 / 2

 r = 2 cm.

The radius of the circle is 2 cm, so the correct answer is Option ‘B”.

(figure attached).