Question

a circle inscribed in a ∆ABC touches the sides AB,BC and CA at P,Q and R,respectively. Find BC,gives that AB =14cm,AR=6cm and RC=7cm.

Answer 1

Answer:

$\red { Length \: of \:BC } \green { = 15\:cm }$

Step-by-step explanation:

A circle inscribed in a ∆ABC touches the sides AB,BC and CA at P,Q and R,respectively.

AB = 14 cm , AR = 6 cm , RC = 7 cm.

AR = AP = 6 cm ,

RC = CQ = 7 cm

$\pink { The \: lengths \: of \:the \: two}$ $\pink {tangents \: from \: an \: external \: point}$

$\pink {to \:a \: circle \: are \: equal }$

AB = 14 cm

=> BP = AB - AP = 14 - 6 = 8 cm

BQ = BP = 8 cm

Now,

$BC = BQ + QC \\= 8\:cm + 7\:cm \\= 15\:cm$

Therefore.,

$\red { Length \: of \:BC } \green { = 15\:cm }$

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