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ABC is a right - angled triangle with ∠ABC = 90°. The centre of the incircle of the given triangle is at O, whose radius is 2 cm. Two more circles wit
Question

ABC is a right - angled triangle with ∠ABC = 90°. The centre of the incircle of the given triangle is at O, whose radius is 2 cm. Two more circles with centres at O1 and O2, touch this circle and the two sides as shown in the figure given below.
Further, MA ∶ MC = 2 ∶ 3.

What is AB + BC equal to?

A.

10cm

B.

12cm

C.

13cm

D.

14cm

Correct option is D



By Pythagoras theorem

Now x = 2
AB+BC = 2x+2+3x+2 = 5x+4 = 5x2+4 = 14

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