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Point P is the center of two concentric circles. PQ = 10.5 and PS = 20.9. RS is tangent to the smaller circle and a chord of the larger circle. What is length of RS to the nearest tenth?

36.1

41.8

31.4

41.4

Point P is the center of two concentric circles. PQ = 10.5 and PS = 20.9. RS is tangent to the smaller circle and a chord of the larger circle. What is length o class=

Verified Answer :

mathmate

In geometry, the very first step is to draw a diagram according to given information, and include ALL given information in the diagram.
This will give a good insight into the problem and  help you solve the problem using all tools you have on hand.

PRS forms an isosceles triangle with legs = PS=20.9.
Let perpendicular from P to RS meet RS at T.
Then PT is the radius of the smaller circle, 10.5.
From the right-triangle PTS, we find, using Pythagoras,
TS=sqrt(PS^2-PT^2)=sqrt(20.9^2-10.5^2)=18.071 (approx.)
Hence length of chord RS is twice TS, = 36.142

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