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A triangle has sides with lengths 13 cm,...

A triangle has sides with lengths 13 cm, 14 cm and 15 cm. A circle whose centre lies on the longest side touches the other two sides. The radius of the circle is (in cm) 15 cm

Text Solution

Verified by Experts

`Ar/_PQR=AR/_POQ+Ar/_POR`
Area of `/_PQR=sqrt(s(s-a)(s-b)(s-c)`
`=sqrt(21*8*7*6)`
`=13/2rcm^2`
Area of`/_POR=1/2*b*h=1/2*14*r=7rcm^2`
`84=(13r)/2+7r`
`84=(13+14)r/2`
`r=56/9cm`
...
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