Question

ABC is a right angled triangle,right angled at B such that BC = 6 cm and AB = 8 cm. A circle with center O is inscribed in $△$ABC. Find the radius of the circle.

• A. 1 cm
• B. 2 cm
• C. 3 cm
• D. 4 cm

Answer 1

The correct option is B

2 cm

By applying Pythagoras theorem

${AB}^2$+ ${BC}^2$ = ${AC}^2$

AC= 10 cm

We know that AX =XY, ZC=YC, BZ=BX
( Length of the Tangents from an external point to the circle is same.)

AB = BX+AY = 8

BC= BZ+YC = 6

Adding the above two equations,

BX+AY+BZ+YC = 8 + 6

BX + BZ = 14– (AY + YC)

2BX= 14 – 10

= 4

Therefore, BX = 2

BX = radius of circle = 2 cm