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# Circle O is a unit circle. Segment AS

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Circle O is a unit circle. Segment AS has length 14/5 and is tangent to circle O at A. If P is the intersection of OS with circle O, find length PS.

Nov 2, 2020

#1
+1019
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AO = PO

PS = [sqrt(AS2 + AO2)] - PO

PS = 1.973213749

Nov 2, 2020
edited by Guest  Nov 2, 2020
#2
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Circle O is a unit circle. Segment AS has length 14/5 and is tangent to circle O at A. If P is the intersection of OS with circle O, find length PS.

Hello Guest!

$$(\overline{PS}+r)^2=2.8^2+r^2\\$$

$$r=1\\ \overline{PS}=1.973$$

!

Nov 2, 2020
edited by asinus  Nov 2, 2020
edited by asinus  Nov 3, 2020
#3
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Hello, asinus!    There are 2 ways to solve this:   1/   Pythagorean theorem (above)

or

2/   AS2 = PS * SN

( N is a point on a circle opposite to point P )

Guest Nov 2, 2020
#4
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Let me correct myself: there are at least 2 ways to solve this...

Guest Nov 2, 2020