Question

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

Answer 1

Answer:

Let the center of two circles be P and Q.Circlres

intersect at A and B

AB cuts PQ perpendicularly at C.

Let CQ be x and AC (half length of chord = l

Apply Pythagoras theorem in triangles APC and AQC

l^2 = 5^2 - (4-x)^2 = 3^2-x^2......(1)

25 - 16 - x^2 + 8x = 9 - x^2

After simplifying you. will get x = 0

put this value of x in any of (1)

you will get l^2= 9

So l=3

Therefore length of the chord = 2l = 2×3 = 6 cm

Answer 2

Answer:

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