Please help guys if you can, this is a really hard problem I am trying to solve
Four circles of unit radius are drawn with centers (1,0),(0,1) ,(-1,0) ,(0,-1) and . A circle with radius 2 is drawn with the origin as its center. What is the area of all points which are contained in an odd number of these 5 circles? (Express your answer in the form "a pi + b" or "a pi - b", where a and b are integers.)
Not sure what you are asking for
There is only one point (0,0) that contains all 5 circles
I worked this out a while back:
http://www.jiskha.com/display.cgi?id=1353876528
To solve this problem, let's break it down step by step:
Step 1: Visualize the scenario
Draw a diagram representing the given circles. This will help you understand the problem better and visualize the area we are interested in.
Step 2: Determine the overlapping regions
Find the areas where the circles intersect with each other. Label these regions as A, B, C, and D. Each region will correspond to a specific number of circles that contain a particular point.
Step 3: Calculate the areas of individual regions
Using geometry, calculate the areas of the regions A, B, C, and D. Since the radius of the smaller circles is given as 1 unit, their area can be directly calculated using the formula A = πr^2.
Step 4: Determine the areas contained in an odd number of circles
By analyzing the overlapping regions, you can determine which points are contained in an odd number of circles. Since we are given five circles in total, we need to find the area covered by an odd number of circles and subtract the area covered by all five circles.
Step 5: Calculate the total area
The total area of all points contained in an odd number of circles can be calculated by adding the areas of regions A, B, C, and D that satisfy the condition of an odd number of circles (i.e., 1, 3, or 5). Finally, subtract the area of the circle with a radius of 2 units centered on the origin.
Step 6: Express the answer
Express the final answer as "a π + b" or "a π - b", where a and b are integers.
Following these steps, you should be able to solve the problem and find the area of the points contained in an odd number of circles.