No 23 â ‹Q23) In triangle ABC, AB = 3, BC = 4, AC = 5, then the - Maths - Circles

Question

No 23

â€‹Q23) In triangle ABC, AB = 3, BC = 4, AC = 5,
then the radius of the circle touches all the three sides is

(a) 2 (b) 1 (c) 4 (d) 3

Varun Rawat · Accepted Answer

Let ABC be the right ∆, in which ∠B = 90°
Now, AC2 = AB2 + BC2   Pythagoras theorem⇒AC2 = 32 + 42⇒AC2 = 9 + 16 = 25⇒AC = 5 cmJoin OA, OB and OC
Draw OD⊥AB, OE⊥BC and OF⊥AC
Let r be the radius of incircle
area of ∆ABC = 12×AB×BC⇒area of ∆OAB + area of ∆OBC + area of ∆OCA = 12×3×4⇒12×3×r + 12×4×r+12×5×r = 6⇒3r2 + 4r2 + 5r2 = 6⇒6r = 6⇒r = 1 cm

No.23 ​Q23). In triangle ABC, AB = 3, BC = 4, AC = 5, then the radius of the circle touches all the three sides is ............... (a) 2 (b) 1 (c) 4 (d) 3

No.23

Q23). In triangle ABC, AB = 3, BC = 4, AC = 5, then the radius of the circle touches all the three sides is ...............

(a) 2 (b) 1 (c) 4 (d) 3