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In fig.(1),ABC is a triangle in …

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In fig.(1),ABC is a triangle in which angle B=90,BC=48cm and AB=14cm. A circle is inscribed in the triangle,whose centre is O.Find radius r of in-circle

Posted by Sinila Anees 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

AC = {tex}\sqrt{\mathrm{AB}^{2}+\mathrm{BC}^{2}}{/tex}
= {tex}\sqrt{14^{2}+48^{2}}{/tex} = {tex}\sqrt{2500}{/tex} = 50 cm

{tex}\angle{/tex}OQB = 90^o {tex}\Rightarrow{/tex} OPBQ is a square

{tex}\Rightarrow{/tex} BQ = r

QA = 14 - r = AR (tangents from a external point are equal in length)

Again PB = r,
PC = 48 - r {tex}\Rightarrow{/tex} RC = 48 - r (tangents from a external point are equal in length)
AR + RC = AC {tex}\Rightarrow{/tex} 14 - r + 48 - r = 50
{tex}\Rightarrow{/tex} r = 6 cm.

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