Question

In the given figure, △ABC s right-angled at B such that BC = 6 cm and AB = 8 cm. A circle with centre O has been inscribed the triangle. OP ⊥ AB, OQ ⊥ BC and OR  ⊥ AC. if OP = OQ = x cm then x = ?

(a) 2 cm 

(b) 2.5 cm 

(c) 3 cm 

(d) 3.5 cm

Answer 1

Correct answer is (a) 2 cm

Given, AB = 8 cm, BC = 6 cm

Now, in △ABC :

AC² = AB² + BC²

\(\Rightarrow\) AC² = (8² + 6²)

\(\Rightarrow\) AC² = (64 + 36)

\(\Rightarrow\) AC = 100

\(\Rightarrow\) AC = \(\sqrt{100}\)

\(\Rightarrow\) AC = 10 cm

PBQO is a square

CR = CQ (Since the lengths of tangents drawn from an external point are equal)

\(\Rightarrow\) \(10=(14-2x)cm\)

\(\Rightarrow\) \(2x=4\)

\(\Rightarrow\) \(x=2cm\)

∴ The radius of the circle is 2 cm.