The radius of the incircle of a triangle is 4 cm and the segments into which one side is divided by the point of contact are 6cm and 8 cm .Determine the other two sides of the triangle.

 

Let the given circle touch the sides AB and AC of the triangle at point E and F respectively and the length of the line segment AF bex.

In ABC,

CF = CD = 6cm (Tangents on the circle from point C)

BE = BD = 8cm (Tangents on the circle from point B)

AE = AF = x (Tangents on the circle from point A)

AB = AE + EB = x + 8

BC = BD + DC = 8 + 6 = 14

CA = CF + FA = 6 + x

2s = AB + BC + CA

x + 8 + 14 + 6 + x

= 28 + 2x

s = 14 + x

Area of ΔOBC = 

Area of ΔOCA =

Area of ΔOAB =

Area of ΔABC = Area of ΔOBC + Area of ΔOCA + Area of ΔOAB

Either x+14 = 0 or x − 7 =0

Therefore, x = −14and 7

However, = −14 is not possible as the length of the sides will be negative.

Therefore, x = 7

Hence, AB = x + 8 = 7 + 8 = 15 cm

CA = 6 + x = 6 + 7 = 13 cm

THUMBS UP PLEASE.

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thnX..!!

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Area Δ ABC = 1/2 . 4 . (AB + BC + AC) = root( s(s – a)(s – b)(s – c))

i.e., 4 s = root( s(s – a)(s – b)(s – c) )

16 s = (s – a) (s – b) (s – c)

i.e., 16 (14 + x) = x X 6 X 8,   i.e., x = 7


Therefore, AB = 15 cm and AC = 13 cm.

plz THUMBS UP

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SECOND ANSWE IS EASY,, 1ST ONE IS TOO LONG

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The radius of the incircle of a triangle is 4 centimetre and the segment into which one side is divided by the point appointed assistant University M determine the two sides of the triangle
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Let the given circle touch the sides AB and AC of the triangle at point E and F respectively and the length of the line segment AF bex. In ABC, CF = CD = 6cm (Tangents on the circle from point C) BE = BD = 8cm (Tangents on the circle from point B) AE = AF = x (Tangents on the circle from point A) AB = AE + EB = x + 8 BC = BD + DC = 8 + 6 = 14 CA = CF + FA = 6 + x 2s = AB + BC + CA = x + 8 + 14 + 6 + x = 28 + 2x s = 14 + x Area of ΔOBC = Area of ΔOCA = Area of ΔOAB = Area of ΔABC = Area of ΔOBC + Area of ΔOCA + Area of ΔOAB Either x+14 = 0 or x − 7 =0 Therefore, x = −14and 7 However, x = −14 is not possible as the length of the sides will be negative. Therefore, x = 7 Hence, AB = x + 8 = 7 + 8 = 15 cm CA = 6 + x = 6 + 7 = 13 cm THUMBS UP PLEASE
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answer
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