I have a question my brother asked me but I need a math expert.

You have two interlocking circles and the radius of circle B goes through the center of circle A and of course the radius of circle A goes through the center of circle B. The radius of each circle is 30 feet. Now, if you draw a line C from the top center of circle A across to the top center of circle B, the line would be 60 feet long and would leave an area below it created by the line C and part of an arc of circle A and part of an arc of circle B. Please give me the area of that space in square feet or the formula for how it's worked. Thanks.

asked by DrBob222
  1. We will describe the problem as follows.

    Two circles A,B of equal radii (r=30') are centred at P, Q, distance r apart.

    Points R and S on circles A, B are such that RS form a common tangent to both circles. Hence PRSQ form a square of side r.

    Arcs are drawn with centre P and Q, radius r, which intersect at point D inside the square.

    Hence Δ PDQ is an equilateral triangle of side r.

    The required area bounded by the side RS , arcs RD and DS will be equal to

    Area of square PRSQ - Area of ΔADQ - area of sector RPD - Area of sector SQD.

    Note that sectors RPD and SQD have centrai angles of (90-60)=30°.

    posted by MathMate
  2. Typo corrections:

    Area of square PRSQ - Area of ΔPDQ - area of sector RPD - Area of sector SQD.

    Note that sectors RPD and SQD have central angles of (90-60)=30°.

    posted by MathMate
  3. Many thanks.

    posted by DrBob222
  4. You're welcome!

    posted by MathMate

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    Show that the function F( x)=∫(from x to 3x)1/t dt is constant on the interval (0, +∞). Okay so I'm not sure if I should use the FTOC Part 1 or something else but this question is just really confusing. I asked my brother and
  2. Math

    FIve years ago Zack would have been three times older than his young brother but five years from now he will only be two times older than his brother. How old is his brother? 25 In other words let x= brothers age so: 3(x-5)=2(x+5)
  3. english

    Question #1 Is the following sentence written correctly? Yes or no? 1. “Hey,” he asked, “who are they?” 2. “No,” she said “that is not painful.” 3. “His mother, he said, “is taking night classes”. 4.
  4. history

    Charlemagne first came to power using which of the following tactics? He allied with his brother to defeat a rival leader. He asked the Pope to name him the Emperor of the West. He named himself Emperor of the West. He allied with
  5. English

    He asked me a question. He asked a question of me. He begged me a question. He begged a question of me. He inquired me a question. He inquired me of a question. (Are the pairs all correct and interchangable? Doe they have the same
  6. English/ History

    In History, we are reading the book _My Brother Sam is Dead_ and one of the questions asked: What did Sam's being home reveal about discipline among the Rebel troops? Please help me understand what the question means, thanks!

    ARE YOU A EXPERT TO HELP STUDENTS ON THEIR HOMEWORK LIKE ME? Bob Pursley is actually more than "a expert." He has become one of the leading experts in homework help on the board. So much so that the "International Council on World
  8. Math

    I am doing Partial Quocients Division for homework. And I need help.But, my mom didn`t learn this method.And my dad`s gone on buisness, my brother doesn`t know how to do it, my other brother is doing his homework and my sister is
  9. English

    Using commas Dr. Perillo, a nutritionist, is an expert on proper eating. "Students, it's important to eat a well-balanced diet," she said. "Yes, but how do we know what the right foods are?" asked one student.
  10. english

    I did a exercise with indirect speech, can anybody check it? 1. "Have you visited the NA?" she asked me. -> She asked me if I had visited the NA. 2. "What do you think of the hotel food?" I asked her. -> I asked her what she

More Similar Questions