Quandaries
and Queries 

Name: wan Who is asking: Student I am trying to find the radius
of an arc. The only things i know about the arc is all referenced from
the line of tangency to the arc. on both sides i have a differnt horizontal
perpendicular distance to the point of tangency. 

Hi Wan, I drew a diagram in the coordinate plane with the point of tangency at the origin O and the tangent line the Xaxis. If a and b are the horizantal and vertical distances from the point of tangency to one of the endpoints of the arc then this endpoint is at (a,b). I called this point Q.
Let P be the midpoint of the line segment OQ and construct a perpendicular to OQ at P meeting the Yaxis at C. Since OQ is a chord of the circle the center lies on the line PC. Since the Xaxis is a tangent to the circle, the center is on the Yaxis. Thus the center of the circle is C. Write the equation of the line PC. It passes through P which has coordinates ^{a}/_{2} and ^{b}/_{2} and has slope ^{a}/_{b}. The center of the circle is the point C(0,r) where this line intersects the Yaxis. The radius of the circle is r. Penny 

