# Finding a geometric relationship.

Problem :

• The point o moves to o' along the x axis to a distance 'x'.

• The point 'a' moves on a circle and reaches 'b' such that oa = o'b. angle subtended by 'a' and 'b' is 'θ '

• The point 'c' moves through the same angle 'θ ' as of a . point 'c' finally reaches point 'd' .

• point 'e' is fixed on the 'y' axis.

I want to find the relation between 'x' and *(ce - de).

This is a physical problem of a crank motion. I am able to find the relation with the help of CAD software but could not establish a geometrical relationship.

• Is the smaller circle tangent to the $y$ axis at $C$? – Blue Jan 7 '18 at 21:05
• @Blue : No, but if it simplifies the case by much then you may assume it. Thanks. – Anshuman Sinha Jan 7 '18 at 21:35