Circle Geometry Questions (1 Viewer)

[Saintly Devil]

Can anyone do these questions?????????

1) Two circles intersect in A and B and the two tangents at A are perpendicular. Are the two tangents at B also perpendicular? Give proof.

2) Two circles intersect in A and B. At A tangents are drawn to each circle, cutting the circles at P and Q. Prove that the triangles PAB and QAB are equiangular.

Appreciate it if u could post the answers up.

Thanx.

 

[spice girl]

1) Yes

Draw the tangents at A, B. Consider the line L, joining the centres of both circles. The whole figure is symmetric about the line L. So, if tangents at A are perpendicular, so are tangents at B. (figure is symmetric, because all circles are symmetric about the line through the centre)

2) Using the alternate segment theorem:
angle BPA = angle BAQ
angle BQA = angle BAP

thus equiangular.