Question

The center of the circle is o and rs=st=4. What is the length of arc rwt

Answer 1

Length of Arc RWT  =   16π/3  The center of the circle is o and rs=st=4 and ∠RST = 120°

Step-by-step explanation:

RT is a chord

∠RST = 120°

=> ∠ROT = 2 * 120°   ( on w side)

=> ∠ROT = 240°  ( on w side)

=> ∠ROT = 360° - 240°  ( on s side)

=> ∠ROT =  120° ( on s side)

Now if we see ΔRST & ΔROT

RT is common

∠RST = ∠ROT

and RS = RT = 4    &  OR = OT  = Radius

=> ΔRST ≅ ΔROT

=> OR = OT = RS = RT = 4 cm

Length of Arc RWT  =  (240°/360°) * 2π R

= (2/3) * 2π * 4

= 16π/3

Length of Arc RWT  =   16π/3

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