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2 Little Semi Circle,can U Find.the AB^2, test your power of reasoning(mr Shape) - Education - Nairaland

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2 Little Semi Circle,can U Find.the AB^2, test your power of reasoning(mr Shape) by Mrshape: 8:22am On Aug 14
Find (AB)^2 in the figure below

Re: 2 Little Semi Circle,can U Find.the AB^2, test your power of reasoning(mr Shape) by Mrshape: 9:22am On Aug 14
No response or is it a case of local man cannot can?

Re: 2 Little Semi Circle,can U Find.the AB^2, test your power of reasoning(mr Shape) by Martinez39: 9:25am On Aug 14
AB² = 96 unit²

1 Like

Re: 2 Little Semi Circle,can U Find.the AB^2, test your power of reasoning(mr Shape) by Boringdraw1: 9:31am On Aug 14
AB^2= 96 unit^2

1 Like

Re: 2 Little Semi Circle,can U Find.the AB^2, test your power of reasoning(mr Shape) by Martinez39: 10:13am On Aug 14
My work, using coordinate geometry.

1) Fix the diagram on a rectangular coordinate system such that point O is at the origin and CD lies on the x-axis. Doing this gives the following coordinates:
O(0, 0), F(4, 0), D(6, 0), E(-3, 0), C(-6, 0)

2) The equation of the circle that yields the bigger semicircle is
x² + y² = 6² ————(1)
and the equation of the circle that yields the smaller semicircle is
(x - h)² + (y - k)² = r² ————(2)

where (h, k) is the center of the circle and r = |AB|/2 is it's radius

3) the smaller semicircle contains the points F(4, 0) and E(-3, 0) therefore the coordinates of both points satisfies eq. (2)
(-3 - h)² + k² = r² ————(3)
and
(4 - h)² + k² = r² ————(4)

Solving (3) & (4) simultaneously, we will discover that h = ½ and substitution into either (3) or (4) yields k² + (49/4) = r²

4) Observe that point (h, k), O(0, 0) and point B are vertices of a right triangle of sides a, b, and c such that
a² = h² + k² = ¼ + k²,
b² = 6², and
c² = r² = k² + (49/4)
and by the Pythagorean theorem, c² + a² = b².

Substituting and solving for , we find that k² = 47/4 and therefore r² = k² + (49/4) = 24


5) r² = |AB|²/4
|AB|² = 4r² = 96 unit²

|AB|² = 96 unit²

1 Like

Re: 2 Little Semi Circle,can U Find.the AB^2, test your power of reasoning(mr Shape) by Mrshape: 10:46am On Aug 14
Boringdraw1:
AB^2= 96 unit^2
96 is correct show ur workings please.
Re: 2 Little Semi Circle,can U Find.the AB^2, test your power of reasoning(mr Shape) by Mrshape: 10:46am On Aug 14
Martinez39:
My work, using coordinate geometry.

1) Fix the diagram on a rectangular coordinate system such that point O is at the origin and CD lies on the x-axis. Doing this gives the following coordinates:
O(0, 0), F(4, 0), D(6, 0), E(-3, 0), C(-6, 0)

2) The equation of the circle that yields the bigger semicircle is

and the equation of the circle that yields the smaller semicircle is


3) the smaller semicircle contains the points F(4, 0) and E(-3, 0) therefore the coordinates of both points satisfies eq. (2)

Solving (3) & (4) simultaneously, we will discover thath = ½ and substitution into either (3) or (4) yields k² + (49/4) = r²

4) Observe that point (h, k), O(0, 0) and point B are vertices of a right triangle of sidea, b, and c such that


5) r² = |AB|²/4
|AB|² = 4r² = 96 unit²

|AB|² = 96 unit²
Good one.
Re: 2 Little Semi Circle,can U Find.the AB^2, test your power of reasoning(mr Shape) by Martinez39: 11:18am On Aug 14
Awaiting more shapes tomorrow.
Re: 2 Little Semi Circle,can U Find.the AB^2, test your power of reasoning(mr Shape) by Mrshape: 11:37am On Aug 14
Martinez39:
Awaiting more shapes tomorrow.
Sure sir
Re: 2 Little Semi Circle,can U Find.the AB^2, test your power of reasoning(mr Shape) by Martinez39: 11:47am On Aug 14
Mrshape:

Sure sir
In that your meme, what's the meaning of "CAN"? grin
Re: 2 Little Semi Circle,can U Find.the AB^2, test your power of reasoning(mr Shape) by Mrshape: 12:35pm On Aug 14
Martinez39:
In that your meme, what's the meaning of "CAN"? grin
I think it means I will not bother attempting, I am not doing again, this is beyond me, in fact local man can not can.
Re: 2 Little Semi Circle,can U Find.the AB^2, test your power of reasoning(mr Shape) by Kkings11: 12:43pm On Aug 14
G'day Mrshape what about yesterday's shape answer
Re: 2 Little Semi Circle,can U Find.the AB^2, test your power of reasoning(mr Shape) by Mrshape: 12:45pm On Aug 14
Kkings11:
G'day Mrshape what about yesterday's shape answer
ok sir I will post it soon
Re: 2 Little Semi Circle,can U Find.the AB^2, test your power of reasoning(mr Shape) by Darivie05: 3:57pm On Aug 14
Martinez39:
My work, using coordinate geometry.

1) Fix the diagram on a rectangular coordinate system such that point O is at the origin and CD lies on the x-axis. Doing this gives the following coordinates:
O(0, 0), F(4, 0), D(6, 0), E(-3, 0), C(-6, 0)

2) The equation of the circle that yields the bigger semicircle is

and the equation of the circle that yields the smaller semicircle is


3) the smaller semicircle contains the points F(4, 0) and E(-3, 0) therefore the coordinates of both points satisfies eq. (2)

Solving (3) & (4) simultaneously, we will discover that h = ½ and substitution into either (3) or (4) yields k² + (49/4) = r²

4) Observe that point (h, k), O(0, 0) and point B are vertices of a right triangle of sides a, b, and c such that


5) r² = |AB|²/4
|AB|² = 4r² = 96 unit²

|AB|² = 96 unit²
Nice solution
Re: 2 Little Semi Circle,can U Find.the AB^2, test your power of reasoning(mr Shape) by Red2C(m): 6:17pm On Aug 14
Martinez39:
My work, using coordinate geometry.

1) Fix the diagram on a rectangular coordinate system such that point O is at the origin and CD lies on the x-axis. Doing this gives the following coordinates:
O(0, 0), F(4, 0), D(6, 0), E(-3, 0), C(-6, 0)

2) The equation of the circle that yields the bigger semicircle is

and the equation of the circle that yields the smaller semicircle is


3) the smaller semicircle contains the points F(4, 0) and E(-3, 0) therefore the coordinates of both points satisfies eq. (2)

Solving (3) & (4) simultaneously, we will discover that h = ½ and substitution into either (3) or (4) yields k² + (49/4) = r²

4) Observe that point (h, k), O(0, 0) and point B are vertices of a right triangle of sides a, b, and c such that


5) r² = |AB|²/4
|AB|² = 4r² = 96 unit²

|AB|² = 96 unit²
Sweeet

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