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 PQR is a right angled triangle right angled at Q.PQ=5cm,QR=12cm.A circle with centre O is inscribed in triangle PQR, touching its all sides.find the radius of the circle.

here triangle PQR is right angled triangle,

PQ= 4cm

QR= 12cm

since circle touches all sides of the triangle, therefore PR is one of the chord of Circle.(more clear by figure)

we know that if a chord subtend a right angle on the circle then the chord is diameter of the circle .. in other word diameter is only chord which subtend 90* on the  circle,

since PR subtend a right angle on the circle i.e. angle PQR= 90*..

thus PR is diameter of the circle.

now in triangle PQR

PR2= PQ2+QR2

PR2=52+122

PR2=25+144

PR2=169

PR2=132

PR=13 cm

therefore D=13cm

  R=13/2 cm= 6.5cm

Required radius of circle is 6.5 cm or 13/2 cm.

HOPE IT IS CLEAR TO YOU NOW

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Ans is wrong and pls add figures when u and questions
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I think you have misunderstood the question. The question says that the circle is inscribed in the triangle which means that the circle is inside the triangle and not the triangle in the circle. The answer you got is correct for what you understood but you will get the correct answer on yahoo answers
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Actually radius is 2cm
​HOW CAN THE SIZE OF CIRCLE BE LARGER THAN THE TRIANGLE
 
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radius =area of the triangle/semi perimeter
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In triangle PQR,
PRsq= PQ sq +QRsq
        = 5*5+12*12
        =25+144=169
PR   = root 169=13 cm

ar PQR=1/2*5*12= 90cm

​ar PQR= ar PQO+ arQOR+ ar POR
​90= 1/2r*PQ + 1/2r* QR +1/2r* PR
90= 1/2r (PQ + QR+ PR)
90=1/2R (5+12+13)
90*2/30=r
r=6cm
 
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This is correct answer

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Dear friend

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What are you looking for?