Two circles of radii 5 cm and 3 cm intersect at two points and the dis

1.	Two circles of radii 5 cm and 3 cm intersect at two points and the distance betweentheir centres is 4 cm. Find the length of the common chord.
Answer» Let O and O' two circle .which intersect in A and B .so, AB is common chord . we know,chord is perpendicularly bisected by line joining of center to its .let line meet at T now,∆ OAT is right angle ∆so,length of OT =√{(5^2 -(x/2)^2 } where x is length of chord again ,for ∆ O' AT length of O'T =√{(3)^2 -(x/2)^2 but here ,length of OT + length of O'T =distance between centre of circles √(25 - x^2/4) +√(9 -x^2/4 ) =4letx^2/4 =r√(25-t) +√(9-t) =4 if we put t = 9then,√(25 -9) +√(9-9) = √16 +0 =4LHS = RHS so, t =9x^2/4 =9x^2 =36 x=6 cm so,length of chord = 6 cm

Two circles of radii 5 cm and 3 cm intersect at two points and the distance betweentheir centres is 4 cm. Find the length of the common chord.

Answer»

Let O and O' two circle .which intersect in A and B .so, AB is common chord .

we know,chord is perpendicularly bisected by line joining of center to its .let line meet at T

now,∆ OAT is right angle ∆so,length of OT =√{(5^2 -(x/2)^2 }

where x is length of chord

again ,for ∆ O' AT

length of O'T =√{(3)^2 -(x/2)^2

but here ,length of OT + length of O'T =distance between centre of circles

√(25 - x^2/4) +√(9 -x^2/4 ) =4letx^2/4 =r√(25-t) +√(9-t) =4

if we put t = 9then,√(25 -9) +√(9-9) = √16 +0 =4LHS = RHS

so,

t =9x^2/4 =9x^2 =36

x=6 cm

so,length of chord = 6 cm