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mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Square ABCD Inside Circle O

Square ABCD lies inside circle O. Square ABCD and circle O are both shaded. Find the area of the shaded region.

Let me see.

1. Find the hypotenuse of the square inside circle O given the lengths to be 2 by 2

2. The hypotenuse is the diameter of circle O.

3. Finding the area of circle O should give me the answer since both figures are shaded.

Yes?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Square ABCD Inside Circle O

Yes, except I'm confused that both shapes are shaded.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Square ABCD Inside Circle O

Yes, except I'm confused that both shapes are shaded.

Bob

A square lies in a circle. The sides of the square are actually line segments for the circle. Both figures are shaded.

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Square ABCD Inside Circle O

Yes, except I'm confused that both shapes are shaded.

Bob

Problem 39; page 37.

I think I have to add the areas.

I must find the hypotenuse if the circle.

NOTE: I NAMED THE CIRCLE USING THE LETTER O.

Let d = diameter.

2^2 + 2^2 = d^2 = hypotenuse.

8 = d^2

2•sqrt{2} = d

diameter = 2r, the radius.

2•sqrt{2} = 2r

2•sqrt{2}/2 = r

sqrt{2} = 2

Let A_r = area of shaded region.

A_r = pi•(sqrt{2})^2 + 2^2

A_r = 2pi + 4

Yes?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Square ABCD Inside Circle O

Again it is a great help to have the page ref.

You have got the diameter correct as root(8)  + root(4) x root(2) = 2root(2)

So the radius is root(2) that's all you need as the shaded area is a circle so youcan forget the square now. You only needed it for that diagonal.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Square ABCD Inside Circle O

Again it is a great help to have the page ref.

You have got the diameter correct as root(8)  + root(4) x root(2) = 2root(2)

So the radius is root(2) that's all you need as the shaded area is a circle so youcan forget the square now. You only needed it for that diagonal.

Bob

Copy.

Shaded area = pi•(sqrt{2})^2

Shaded region = 2pi.

Yes?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Square ABCD Inside Circle O

yes.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Square ABCD Inside Circle O

yes.

Bob

Beautiful.  Math is great. I never get tired of this stuff. Yes, I am a math nerd and proud to be. I enjoy learning stuff that others hate and fear. Math has a way of humbling the proud. This is why students hate it.

Last edited by mathxyz (2024-05-18 06:13:39)