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