Question

The radii of two concentric circles are 17cm and 10cm. A line segment PQRS cuts the larger circle at P and S and

the smaller circle at Q and R. If QR= 12cm, find the length of PQ​

Answer 1

Answer:

A

9 cm

Given−Oisthecentreoftwoconcentriccirclesofradii10cmand17cm.ThelinePQRSintersectstheoutercircleatP&SandtheinnercircleatQ&R.QR=12cmTofindout−PQ=?Solution−WejoinOP,OS,OR,OQ.∴OP=OS=17cm&OQ=OR=10cm.AlsowedropaperpendicularONfromOtoPQRS.ONquadmeetsPQRSatN.NowON⊥QRatN.∴NisthemidpointofQRsincetheperpendicular,droppedfromthecenterofacircletoitsanychordbisectsthelatter.∴QN=21QR=2