Question

Consider circle H with a 6 centimeter radius. If the length of minor arc ST is

11
2
π, what is the measure of ∠RST? Assume RS ≅ TS.

Answer 1

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Answer 2

`\angle RST=(\pi)/(12)`

Explanation:

Given a circle H with radius 6 cm and the length of minor arc ST is
`(11)/(12)\pi`. we have to find the measure of ∠RST.

Also RS ≅ TS.

When two chords are are congruent then the arc formed with these chords are also congruent.

∴
`arc(RS)=arc(TS)=(11)/(12)\pi`

Now, as circumference of circle or total arc equals to 2π

⇒
`arc(RT)=2\pi-ar(RS)-arc(ST)=2\pi-(11)/(12)\pi-(11)/(12)\pi=(\pi)/(6)`

As, angle formed at the center is twice the angle subtended at the circumference.

⇒
`\angle RST=(1)/(2) *\angle RHT=(1)/(2) *(\pi)/(6)=(\pi)/(12)`

`\angle RST=(\pi)/(12)`