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The diagram shows a circle C1 touching a circle C2 at a point X. Circle C1...

The diagram shows a circle C1 touching a circle C2 at a point X. Circle C1 has center A and radius 6 cm, and circle C2 has center B and radius 10 cm. Points D and E lie on C1 and C2 respectively and DE is parallel to AB. Angle DAX = 1/3? radians and angle EBX = ? radians.

1) By considering the perpendicular distances of of D and E from AB, show that the exact value of ? is sin^-1 (3*sqrt(3)/10)

2) Find the perimeter of the shaded region, correct to 4 significant figures.

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