# Monthly Archives: November 2014

## Small Circle

A circle is inscribed in a sector of a circle of radius (as shown). What is the radius of the small circle? Source: NCTM Mathematics Teacher, February 2006 SOLUTION is the angle bisector of because is equidistant from and . Triangle … Continue reading

## Socks of Same Color

Sean has a drawer containing black socks, brown socks, blue socks, and green socks, all loose and not properly paired. Sean takes socks out of the drawer at random without replacement, in the dark. How many socks must Sean take … Continue reading

## Smallest Side of a Right Triangle

The sides of a right triangle are all integers. Two of them are odd numbers that differ by . What is the smallest possible value for the third side? Source: NCTM Mathematics Teacher, February 2006 SOLUTION We … Continue reading

## Seventh Student Score

Six students in a small class took an exam. The average of their grades was . The seventh student in the class was ill that day and took the exam another day. When this student’s score was included, the class … Continue reading

## XYZ=4000

How many ordered triples of positive integers satisfy ? Source: NCTM Mathematics Teacher 2006 SOLUTION This problem is similar to the problem “Triple ABC” posted on 9/14/2012, nevertheless a different solution is offered here. Given that , the positive integers … Continue reading

## Length of Segment

In triangle and . Point on divides it into segments of length and . What is the length of segment ? Source: NCTM Mathematics Teacher 2006 SOLUTION Using the Heron’s area formula to calculate the area of triangle Area = … Continue reading