a circle is inscribed in a triangle of sides 8,15 and 17cm . find the radius of the circle
Answers
Answered by
4
Let ABC be the triangle with AB =8 cm, BC = 15 cm and AC = 17cm.
Consider, 82 + 152 = 64 + 225 = 289
That is 82 + 152 = 172
Hence ABC is a right angled triangle
Therefore area of ΔABC = (1/2) × 8 × 15 = 60 sq cm
Let r be the radius of the incircle whose centre is I.
Now consider, ar(ΔAIB + ΔBIC + ΔCIA) = [(1/2) × AB × r] + [(1/2) × BC × r] + [(1/2) ×AC × r]
( 1/2 ) × r × ( 8 + 15 + 17 ) = ( 1/2 ) × r × (40)
= 20r
But, ar(ΔAIB + ΔBIC + ΔCIA) = ar(ΔABC )= 60 sq cm
Hence 20r = 60
r = 3 cm
Consider, 82 + 152 = 64 + 225 = 289
That is 82 + 152 = 172
Hence ABC is a right angled triangle
Therefore area of ΔABC = (1/2) × 8 × 15 = 60 sq cm
Let r be the radius of the incircle whose centre is I.
Now consider, ar(ΔAIB + ΔBIC + ΔCIA) = [(1/2) × AB × r] + [(1/2) × BC × r] + [(1/2) ×AC × r]
( 1/2 ) × r × ( 8 + 15 + 17 ) = ( 1/2 ) × r × (40)
= 20r
But, ar(ΔAIB + ΔBIC + ΔCIA) = ar(ΔABC )= 60 sq cm
Hence 20r = 60
r = 3 cm
Similar questions