[Math] Find the radius of a circle inscribed in a pendant

circlesgeometrytrigonometry

The shape shown in Figure 1 is a pattern for a pendant. It consists of a sector OAB of a circle centre O, of radius 6 cm, and angle $AOB = \frac{\pi}{3}$. The circle C, inside the sector, touches
the two straight edges, OA and OB, and the arc AB as shown.

Find the radius of the circle C.

I have no clue how to approach this. Help please.

Best Answer

What about now?

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still no clue?

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