Question

Two circles of radii 10cm and 17cm intersect at two points and distance between their centres is 21 cm. Find length of the common chord.i have an exam tomorrow... plzz help :)

Answer 1

take the point of intersection of common chord and distance between center as P.

one center as O and other as O' .

and the point of intersection of circles A and B.

Now proove triangle AOO' and BOO' congurent .

By cpct angle AO'P=BO'P

now proove triangle AO'P and triangle BO'P congurent by SAS criteria.

By cpct angle APO' =BPO' but their sum is 180

so angle APO' =900.

take PO' as x and PO as 21-x

now in triangle APO' 102= x2+AP2 ===>AP2=102-X2 ---(1)

in traingle AOP 172=(21-x)2+AP2

================>AP2=172-PO2 ---(2)

By (1) and (2)

172-(21-x)2=102-x2

now by solving we get the value of x=6

now find the value of AP

======> AP2=102-x2

AP=8

as AP=8 so AB=16

hence the lenght of common chord is 16cm.