Question

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
41.4
31.4
41.8

Answer 1

I think it is C

Answer 2

well the tangent RS and the radius PQ are perpendicular to each other, so you need pythagoras

\[PS^2 = QS^2 + PQ^2\]

then you need to know the perpendicular from the centre to the chord bisects the chord

so

RQ = QS or RS = 2QS

hope it helps

Answer 3

and I don't think its C

Answer 4

i got 547 30/50

Answer 5

547 30/50^2 is 299274.6436

Answer 6

well using pythagoras' theorem you need to find QS

manipulating the equation

\[QS^2 = PS^2 - PQ^2\]

so

\[QS^2 = 20.9^2 - 10.5^2\]

so start by finding QS

then double it to get RS

Answer 7

20.9^2-10.5^2= 326 14/25

Answer 8

326 14/25^2 is 106641.4336

Answer 9

you don't want to square 326.56 you want to (or should want to) take the *square root*

Answer 10

so 18.0709712

Answer 11

and as campbell posted (see up above), that is 1/2 of the length you want.

Answer 12

so do i add 1/2?

Answer 13

or do 18.0709712^2?

Answer 14

multiply by 2

Answer 15

so that is QS

now the perpendicular line from the centre, PQ, bisects RS.

so RS = 2 x QS

so you know QS, just double it... to find RS

Answer 16

or add to itself

Answer 17

36.1419424

Answer 18

now round to the nearest tenth

Answer 19

so 36.1?

Answer 20

yes

Answer 21

that's correct... now round it to 1 decimal place

Answer 22

36.1?

Answer 23

correct

Answer 24

what message?