Thursday, December 11, 2014

A math problem from a BC student

I got a problem from a kid of my friend. I want to share with you.

Here is the problem:


We are asking to find the x-coordinate of point R and it is the length of OR. 

Solution 1:
Find the mid-point, C on the diameter of the semicircle. Then connect C and S, as shown above.
Because S is the point with greatest y-coordinate, we know CS is the radium and CS is 4. We also know CS is perpendicular to RC, then OC = 1.5 which is the x-coordinate of S. RC is the radium of the semicircle which is 4, so OR = RC - OC = 4 - 1.5 = 2.5. Point R is on the left side of O, so the x-coordinate of R is -2.5.

The right answer is (E)

Solution 2:
Draw a parallel-line of y-axis from S  and cut the x-axis on Point C. We know from the properties of circle CS is the radium, which is 4, the y-coordinate of S and OC is 1.5 which is the x-coordinate of S. RC is the radium of the semicircle which is 4, so OR = RC - OC = 4 - 1.5 = 2.5. Point R is on the left side of O, so the x-coordinate of R is -2.5.

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