Question

Three circles with centers A,B and C touch each other externally. AB = 10cm, Bc = 8cm and AC = 6cm. Find the radius of the circle with center A.
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Answer 1

Step-by-step explanation:

Given: ABC is a triangle with AB = 10 cm, BC= 8 cm, AC = 6 cm. Three circles are drawn with centre A, B and C touch each other at P, Q and R respectively.

So, we need to find the radii of the three circles.

Let,

PA = AQ = x

QC = CR = y

RB = BP = z

So , we have

x + z = 10 ….. (i)

z + y = 8 …… (ii)

y + x = 6 ……. (iii)

Adding all the three equations, we have

2(x+y+z)=24

x + y + z = 24/2 = 12 ….. (iv)

Subtracting (i), (ii) and (iii) from (iv) we get

y = 12 – 10 = 2

x = 12 – 8 = 4

z = 12 – 6 = 6

Thus, radii of the three circles are 2 cm, 4 cm and 6 cm

Answer 2

Answer:

Three circles are drawn touching each other with the vertices as their centres. Find the radii of the three circles. Solution Show Solution. Let the radii of ...