Question

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)​

Answer 1

Radius of circle = 56/9  cm

Step-by-step explanation:

Triangle has three sides

13 , 14 , 15

s = (13 + 14 + 15)/2  = 21

Area of triangle PQR= √21(21-13)(21-14)(21-15)

= √21 * 8 * 7 * 6

= √7 * 3 * 2 * 2 * 2 * 7 * 2 * 3

= 7 * 3 * 2 * 2

= 84

join PO

Area of PQR = Area of POQ +  Area of POR

R = radius of Circle

Area of Triangle = (1/2) PQ * R   + (1/2)PR  * R

= (1/2) 13R  + (1/2) 14R

= 27R/2

27R/2 = 84

=> R = 168/27

=> R = 56/9

Radius of circle = 56/9  cm

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