GregMat+ quant problem help

[sathiya_007]

I might have made the image shabbier, but really wanted to know where I went wrong with my steps.
gn; r=5 and equi. triangle and regular pentagon inscribed in a circle.

arc_length AB = angle subtended to the center/360 * 2* pi * r

To find angle subtended by both A & B, through regular polygons and angles formula, deduced that half of B is 54 and half of A is 30.
Now drawing a line from A to B to complete imaginary triangle.
→ angle subtended by center is 96 deg

now 96/360 * 2* pi *5 = 8 * pi/3 which is > 2 * pi /3

So chose choice A. but turns out answer is C

help me out on this! thanks in advance

[HoldMyBeer]

theta = 24

[vidishas99]

You can do what @HoldMyBeer has done, but I find this method easier:
The triangle divides the circle into 3 equal arcs of length = 2* pi* r /3 = 10pi/3
The pentagon divides the circle into 5 equal arcs of length = 2* pi* r/5 = 2pi
Let the common point shared by the triangle and pentagon on the circle be ‘C’
arc AB = arc CAB - arc CA = 2 x 2pi - 10pi/3 = 4pi - 10pi/3 = 2pi/3
Ans. C

[Jeet]

@vidishas99 this is a really smart way of solving it, thanks for sharing. Saves a lot of time!

[shoikot1151153]

oh!! I love this method. thanks a lot.