Question

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

Answer 1

Draw the two intersecting circles and label as follows;

Circle O with radius 8;  circle P with radius 10

AB is chord of intersection and has length = 12

I point on the chord where the radii of the two cirlcles

  will meet

Radius drawn perpendicular to a chord will bisect the chord

You now have four right triangles formed by the radii of each

circle with the perpendicular drawn from each center point

to the chord of intersection,  we will use one triangle from

each circle

OB = 8, BI = 6, find OI by Pythagorean Theorem

      BI2  +  OI2  =  OB2               

       36  +  OI2  =  64

                 OI2   =  √ 28

                 OI   =  5.292

BP = 10,  BI = 6, find PI

This is a 3 - 4- 5 right triangle: 6, PI = 8, 10

Therefor the distance between the centers:

   PO = OI + BI

   PO = 5.292 + 8

  PO = 13.292  ;  Your answer would be : 4


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