There are two concentric circles such that the area of the outer circle is four times the area of the inner circle. Let A, B and C be three distinct points on the perimeter of the outer circle such that AB and AC are tangents to the inner circle. If the area of the outer circle is 12 square centimeters then the area (in square centimeters) of the triangle ABC would be

In the figure alongside, PQRS is a rectangle and QLMN is a square equal in area to the rectangle such that QL is perpendicular to SQ. If SL measures  √84 cm and the lengths of PQ and PS are whole numbers (when measured in cm), what is the measure of SM (in cm)

In a rectangle ABCD, P and Q are points on AD and DC such that triangle BPQ is equilateral. Which of the following is true of the ratio r = AB : BC?