In the figure, ray PQ touches the circle at point Q. If PQ =12, PR = 8, then find PS.

Answer

PS = 18 and RS = 10

Explanation

Ray PQ is tangent touching the circle at point Q and line PRS is secant intersecting the circle at points R and S.
`:.PQ^(2)=PRxxPS" " "……."(" By tangent secant segments theorem ")`
`:.12^(2)=8xxPS`
`:.PS=(12xx12)/(8)`
`:.PS=18`
PR+RS=PS`" " " ........"(" P-R-S ")`
`:.8+RS=18`
`:. RS=18-8`
`:.RS=10`