An equilateral triangle surrounds a circle of radius 10 cm and is itself surrounded by a larger circle Find the radius of the bigger circle?

Make a sketch of the situation. From a corner of the equilateral triangle draw a radius of the large circle, and from an adjacent side draw a radius of the smaller circle. You should have formed a small right-angled triangle with a known side of 10cm. and known angles of 30o, 60o and 90o. (The interior angles of an equilateral triangle are each 60o.) The hypotenuse is the unknown radius of the larger circle. But since cos 60 = 0.5, it is evident that the hypotenuse is 20cm. long.