Question

ABC is a triangle with AB = 10 cm, BC = 8 cm and AC = 6 cm (not drawn to scale). Three circles are drawn touching each other with the vertices as their centers. Find the radii of the three circles.​

Answer 1

Step-by-step explanation:

✿ᑫᑌᗴՏTIOᑎ:-

ABC is a triangle with AB = 10 cm, BC = 8 cm and AC = 6 cm (not drawn to scale). Three circles are drawn touching each other with the vertices as their centers. Find the radii of the three circles.

✿ᗩᑎՏᗯᗴᖇ:-

◉ՏOᒪᑌTIOᑎ:-

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

$So, \: we \: need \: to \: find \: the \: radii \: of \: the \: \: three \: circles$

$Let,\\ PA = AQ = x \\ QC = CR = y\\ RB = BP = z\\ So , \\ we \: have \\ x + z = 10 ….. (i) \\ z + y = 8 …… (ii) \\ y + x = 6 ……. (iii)$

$Adding \: all \: the \: three \: equations, \: we \: have$

$2 \: (x+y+z) \: = \: 24$

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

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

$\: y = 12 – 10 = 2\\ x = 12 – 8 = 4 \\ z = 12 – 6 = 6$

$Thus, \: radii \: of \: the \: three \: circles \: \\ are \: 2 \: cm, \: 4 \: cm \: and \: 6 \: cm.$

Answer 2

Step-by-step explanation:

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