Two circles of radius r and r' touch externally at P APB is a secant intersecting the circles respectively - Maths - Circles

Question

Two circles of radius r and r' touch externally at P APB is a
secant intersecting the circles respectively at A and B(other than
P) Prove that PA/PB = r/r'

Duke Biswass · Accepted Answer

<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/discuss_editlive/5474837/2013_09_28_13_11_03/Untitled%20png">
Triangles OAP and O'BP are similar
so, PA/PB = OA/O'B = r/r'

Two circles of radius r and r' touch externally at P. APB is a secant intersecting the circles respectively at A and B(other than P). Prove that PA/PB = r/r'