Question

The radii of two concentric circles, centered at O are 19cm and 10cm. POQ is the diameter of the bigger circle. QR is a chord in the bigger circle drawn tangential to the small circle touching it at S. Find the length of the chord PR of the bigger circle.​

Answer 1

Step-by-step explanation:

Fromthefigure

ODistheradiusofsamllercircle

andBDisthetangenttothesmallercircle

so,OD⊥BD

∴∠ODB=90

∘

and,

InthebiggercirclePisapointinthesemi−circleofthebiggercircle

∴∠APB=90

∘

InΔABPandΔOBD

∠APB=∠ODB=90

∘

∠ABP=∠ODB(common)

ΔABP∼ΔOBD(AAsimilarity)

Now,

OD

AP

​

=

OB

AB

​

8

AP

​

=

13

26

​

AP=2×8

=16 cm

​