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In the figure , O is the same of the cir...

In the figure , O is the same of the circle. From point R, seg RM and seg RN are tangent segments touching the circle at M and N. If OR = 10cm and radius of the circle = 5 cm, then
(i) What is the length of each tangnet segment ?
(iii) What si the measure of `/_MRO ` ?
(iii) Whatis the measure of `/_ MRN ` ?

Text Solution

Verified by Experts

The correct Answer is:
Length of each tangent segment is `5sqrt(3)` cm
In `triangle OMR`,
`/_OMR=90^(@)" " "………"(" Tangent theorem ")`
`:.` Pythagoras theorem,
`OR^(2)=OM^(2)+MR^(2)`
`:.10^(2)=5^(2)+MR^(2)`
`:. MR^(2)=100-25`
`:. MR^(2)=75`
`:.MR=5sqrt(3) cm " " "……."(" Taking square roots of both the sides ")`
`RM=RN=5sqrt(3) cm " " "........"(" Tangent segment theorem ")`
Length of each tangent segment is `5sqrt(3)` cm.
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