Answer:
[tex]\angle RST=\frac{\pi}{12}[/tex]
Step-by-step explanation:
Given a circle H with radius 6 cm and the length of minor arc ST is [tex]\frac{11}{12}\pi[/tex]. 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.
∴ [tex]arc(RS)=arc(TS)=\frac{11}{12}\pi [/tex]
Now, as circumference of circle or total arc equals to 2π
⇒ [tex]arc(RT)=2\pi-ar(RS)-arc(ST)=2\pi-\frac{11}{12}\pi-\frac{11}{12}\pi=\frac{\pi}{6}[/tex]
As, angle formed at the center is twice the angle subtended at the circumference.
⇒ [tex]\angle RST=\frac{1}{2} \times\angle RHT=\frac{1}{2} \times\frac{\pi}{6}=\frac{\pi}{12}[/tex]
[tex]\angle RST=\frac{\pi}{12}[/tex]
