# Monthly Archives: January 2015

## Distance Between Two Points

If two points are selected at random from the interval , what is the probability that the distance between them is less than one fourth? Source: NCTM Mathematics Teacher, February 2006 SOLUTION Consider two points and on the interval. Create … Continue reading

## Ice-Cream Cone

An ice-cream cone’s height is three times its diameter. Two spherical scoops of ice cream with the same diameter as the cone are packed into the cone, filling it completely. Some ice cream bulges above the cone’s top. What percent … Continue reading

## Three Tangent Circles

A circle is inscribed in an equilateral triangle with a side of length . Three circles are drawn externally tangent to this circle and internally tangent to two sides of the triangle. Three more circles are drawn externally tangent to … Continue reading

## Sum of Three-Digit Integers

What is the sum of all the positive three-digit integers that can be formed from the digits , and ? Note that the same digit can appear more than once. Source: NCTM Mathematics Teacher, February 2006 SOLUTION We can make … Continue reading

## Inscribed Circle of Equilateral Triangle

The circumference of a circle circumscribing an equilateral triangle is units. Find the number of square units in the area of the circle inscribed in the same triangle. Source: NCTM Mathematics Teacher, February 2006 SOLUTION In equilateral triangle , angle … Continue reading

## Area of Inscribed Circle

The perimeter and area of a triangle are inches and square inches, respectively. What is the area in square inches of a circle inscribed in the triangle? Source: NCTM Mathematics Teacher, February 2006 SOLUTION area of area of area of … Continue reading

## Four Circles

In the diagram, two of the three dark shaded circles have diameters of units, and the third has a diameter of . What must be the length of the diameter of the white shaded circle to make the sum of … Continue reading

## Up or Right

Starting at the point on the coordinate plane, a pin can be moved either to point or to point . If the pin starts at and is moved to , what is the probability that it passed through ? Source: … Continue reading

## Bookshelf

A bookshelf is inches long and contains books each inches thick. If each book were half an inch thinner, the shelf would hold six more of the same book. What is ? Source: NCTM Mathematics Teacher, February 2006 SOLUTION Substitute … Continue reading

## Fast Clock Slow Clock

When minutes elapse on a correct clock, minutes register on clock (fast), and only minutes register on clock (slow). If later in the day, clock reads and clock reads , what was the correct time when the two clocks were … Continue reading