Question

two circles of radii 5cm and 3cm intersect at two parts and distance between their centres is 4cm . ​

Answer 1

Question:

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

Answer:

Let the common chord be AB and P and Q be the centers of the two circles.

∴AP=5cm and AQ=3cm.

PQ=4cm        ....given

Now, segPQ⊥chord AB 

∴AR=RB=21AB        ....perpendicular from center to the chord, bisects the chord

Let PR=xcm, so RQ=(4−x)cm

In △ARP,

AP2=AR2+PR2

AR2=52−x2       ...(1)

In △ARQ,

AQ2=AR2+QR2

AR2=32−(4−x)2     ...(2)

∴52−x2=32−(4−x)2      ....from (1) & (2)

25−x2=9−(16−8x+x2)

25−x2=−7+8x−x2

         32=8x

       ∴x=4

Substitute in eq(1) we get,

Step-by-step explanation:

hope it helps you

and pls for next time write whole question