ABC is a right-angled triangle with AB=8cm and BC= 6 cm. A circle with centre O has been inscribed inside the triangle. Calculate the value of r the radius of the inscribed circle.

The correct answer is: Hence, the radius of the inscribed circle is 2 cm

                                                     
Given BC = 6 cm and AB = 8 cm
Applying Pythagoras theorem in △ABC

AC² = BC² + AB²

AC² = 6² + 8²

AC² = 100

AC= 10 cm

Let OP = OR = OQ = r
We know that two tangents drawn from an external point to a circle are equal in measure.
So, BP = BQ, CQ = CR and AP = AR
Also, OP and OQ are radii of the circle. OP ⊥ AB and OQ ⊥ BC and ∠B = 90° (given)
Hence, we can conclude that BPOQ is a square.
Thus, BP = BQ = r (sides of a square are equal)
So, AR = AP = AB – BP

AR = AP = 8 – r

CR = CQ = BC – BQ

CR = CQ = 6 – r

Now, AR + CR = AC

8 – r + 6 – r = 10

14 – 2r = 10

4 = 2r

r = 2 cm
Final Answer:
Hence, the radius of the inscribed circle is 2 cm