Question

Two circles of radii 5cm and 3cm intersect at two points and the distance between their centers is 4cm . find the length of the common chord​

Answer 1

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 ) =4

let

x^2/4 =r

√(25-t) +√(9-t) =4

if we put t = 9

then,

√(25 -9) +√(9-9) = √16 +0 =4

LHS = RHS

so,

t =9

x^2/4 =9

x^2 =36

x=6 cm

so,

length of chord = 6 cm

Step-by-step explanation: