Question

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

Options

• 2 cm

• 2.5 cm

• 3 cm

• 3.5 cm

Answer 1

2 cm

Explanation:

AC² = AB² + BC²

= 8² + 6² 

= 64 + 36 

= 100

⇒ `AC = sqrt(100)  cm`

= 10 cm

CR = CQ

= (BC – BQ) 

= (6 – x) cm

AR = AP

= (AB – BP)

= (8 – x) cm

AC = (AR + CR)

= [(8 – x) + (6 – x)] cm 

= (14 – 2x) cm

⇒ (14 – 2x) = 10

⇒ 2x = 4

⇒ x = 2 cm