Answered

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.

Verified Answer :

MissPhiladelphia

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Answer:

\(\angle RST=\frac{\pi}{12}\)  

Step-by-step explanation:

Given a circle H with radius 6 cm and the length of minor arc ST is \(\frac{11}{12}\pi\). 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.

∴ \(arc(RS)=arc(TS)=\frac{11}{12}\pi\)

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

⇒ \(arc(RT)=2\pi-ar(RS)-arc(ST)=2\pi-\frac{11}{12}\pi-\frac{11}{12}\pi=\frac{\pi}{6}\)

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

⇒ \(\angle RST=\frac{1}{2} \times\angle RHT=\frac{1}{2} \times\frac{\pi}{6}=\frac{\pi}{12}\)

\(\angle RST=\frac{\pi}{12}\)  

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