Q) In the given figure, △ABC is a right triangle in which∠B = 90º, AB = 4 cm and BC = 3 cm. Find the radius of the circle inscribed in the triangle ABC.

(Q27 A – 30/1/3 – CBSE 2026 Question Paper)

Ans: 

Step 1: GIvne that Δ ABC is right-angled at B, AB = 4cm, BC = 3cm

∴ By Pythagoras theorem, AC² = AB² + BC²

∴ AC² = (4)² + (3)² = 16 + 9 = 25

∴ AC = 5 cm

Step 2: Next, since all sides of triangles touch the circle, let’s mark these touch points as P, Q and R

∵ it is given that ∠ B = 90⁰

and since Radii are perpendicular to tangents,

∴ ∠ P and ∠ Q = 90⁰

∴  OPBQ is a sqaure

Let’s consider radius of the circle is “r”, ∴ OP = OQ = r

∴ BP = BQ = r     (∵ OPBQ is a sqaure)

Step 3: ∵  AP = AB – BP

∴ AP = 4 – r

Similarly, CQ = BC – BQ 

∴ CQ = 3 – r

Step 4: Now, by tangent property of circle, tangents drawn from an extrenal point are equal

∴ AP = AR = 4 – r

and CQ = CR = 3 – r

Step 5: From the diagram, AC = AR + CR

∴ 5 = (4 – r) + (3 -r)

∴ 5 = 7 – 2 r

∴ 2 r = 7 – 5 = 2

∴ r = 2/2 = 1 cm

Therefore, the radius of the inscribed circle is 1 cm.

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