







Two circles 
20111204 

From Luke: Two fixed circles intersect at A and B.
P is a variable point on one circle.
PA and PB when produced meet the other circle at M and N respectively.
Prove that MN is of constant length.
Thanks!
p.s. I also sent the question with a figure via email. Answered by Chris Fisher. 





Circle Geometry 
20070814 

From Robin: In a triangle ABC, angle A=75 and B=60. A circle circumscribes the triangle. The tangents of the at points A and B meet in a point D outside the circle. Show that ABD is an isosceles triangle with a right angle at D. Diagram included. Answered by Stephen La Rocque. 





Circle Geometry III 
20070717 

From Sean: Two rays are drawn from the same point A outside a circle, and intersect the circle as shown in the picture. Prove that the measure of angle A is onehalf the difference between the measures of arcs BD and CE. Answered by Stephen La Rocque. 





Circle Geometry II 
20070717 

From Sean: Let M be a point outside a circle, and let a line through M be tangent to the circle at point P. Let the line through M and the center of the circle intersect the circle in points Q, R.
Prove that │PM│^{2} = │MQ│ x │MR│ Answered by Stephen La Rocque. 





Circle Geometry  Quadrilateral circumscribing a circle 
20070717 

From Sean: Four lines are tangent to a circle that form a quadrilateral. It appears that the quadrilateral is a trapeziod but this is not a given. Prove that the combined lengths of two opposing sides of the quadrilateral are equal to the combined lengths of the other two opposing sides of the quadrilateral. Answered by Stephen La Rocque. 

