please solve this question for me ABC is a triangle with AB=10cm , BC=8cm - Maths -

Question

please solve this question for me
ABC is a triangle with AB=10cm , BC=8cm , AC=6cm Three circles
are drawn touching each other, with the vertices as their centres
Find the radii of the three circles

Shridhar Kaushik · Accepted Answer

Let the radii of circles with centre A, B, C be x cm, y cm and z cm respectively

Given: AB = 10 cm, BC = 8 cm, AC = 6 cm

⇒ x + y = 10 ........... (1)

y + z = 8 ........... (2)

x + z = 6 ........... (3)

Adding (1), (2) and (3) we get

x + y + y + z + x + z = 10 + 8 + 6

⇒ 2 (x + y + z) = 24

$\Rightarrow x + y + z = \frac{24}{2} = 12 ......... (4)$

from (1) and (4) we get

10 + z = 12

⇒ z = 12 – 10 = 2

from (2) and (4) we get

x + 8 = 12

⇒ x = 12 – 8 = 4

from (3) and (4) we get

y + 6 = 12

⇒ y = 12 – 6 = 6

Hence the radii of the circles are 2 cm, 4 cm and 6 cm

please solve this question for me...... ABC is a triangle with AB=10cm , BC=8cm , AC=6cm.Three circles are drawn touching each other, with the vertices as their centres.Find the radii of the three circles.

please solve this question for me......

ABC is a triangle with AB=10cm , BC=8cm , AC=6cm.Three circles are drawn touching each other, with the vertices as their centres.Find the radii of the three circles.