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Let A be (0, 0) and B be (10, 0). A semicircle is constructed with AB

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Bunuel
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Let A be (0, 0) and B be (10, 0). A semicircle is constructed with AB [#permalink] New post  08 Oct 2021, 08:15
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Let A be (0, 0) and B be (10, 0). A semicircle is constructed with AB as diameter, and C is a point on the circumference such that BC = 8 cm. What are the coordinates of point C?

(A) (10, 8)
(B) (4.4, 5.6)
(C) (2.8, 6.4)
(D) (6.4, 3.6)
(E) (3.6, 4.8)
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stne
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Let A be (0, 0) and B be (10, 0). A semicircle is constructed with AB [#permalink] New post  17 Oct 2021, 04:13
Bunuel wrote:
Let A be (0, 0) and B be (10, 0). A semicircle is constructed with AB as diameter, and C is a point on the circumference such that BC = 8 cm. What are the coordinates of point C?

(A) (10, 8)
(B) (4.4, 5.6)
(C) (2.8, 6.4)
(D) (6.4, 3.6)
(E) (3.6, 4.8)



We know that the distance between two points whose coordinates are \((x_1,y_1)\) and \((x_2, y_2)\) is given by

\(\sqrt{(x_2-x_1)^2 + (y_2 -y_1)^2}\)..... \((i)\)

We already know \((x_1,y_1)= (10,0) \)

Used the options to find the other point .

if \((x_2, y_2)= (3.6,4.8) \)

\(\sqrt{(3.6 -10)^2 + (4.8 -0)^2}\) ..... using \((i)\)

Then \(\sqrt{(-6.4)^2 + (4.8)^2}\)

\(\sqrt{40.96+ 23.04)} = \sqrt{64} = 8 \)

Only E gives the required distance.

Ans-E

Hope it's clear.
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WadderBoi
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Re: Let A be (0, 0) and B be (10, 0). A semicircle is constructed with AB [#permalink] New post  17 Oct 2021, 11:43
I used a different approach to solve the equation. I created the midpoint D and the possible distance of CD is gonna be 5 (radius = 5) and created one equation and another with the distance of BC. But It seems to be quite a lengthy approach. Does any one have any better suggestion?
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Re: Let A be (0, 0) and B be (10, 0). A semicircle is constructed with AB [#permalink] New post  17 Oct 2021, 20:29
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Bunuel wrote:
Let A be (0, 0) and B be (10, 0). A semicircle is constructed with AB as diameter, and C is a point on the circumference such that BC = 8 cm. What are the coordinates of point C?

(A) (10, 8)
(B) (4.4, 5.6)
(C) (2.8, 6.4)
(D) (6.4, 3.6)
(E) (3.6, 4.8)



Center of the circle is (5,0)
Radius of the circle is 5 units.

Equation of the circle= (x-5)^2+(y-0)^2= 5^2

(x-5)^2+(y-0)^2= 25
Any point on the circumference will satisfy the equation.

A- (10-5)^2+(8-0)^2=25
LHS is not equal to RHS.

and so On.

Only E satisfies the equation.

Answer is E.
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Bunuel
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Re: Let A be (0, 0) and B be (10, 0). A semicircle is constructed with AB [#permalink] New post  03 Nov 2021, 07:51
Expert Reply
Bunuel wrote:
Let A be (0, 0) and B be (10, 0). A semicircle is constructed with AB as diameter, and C is a point on the circumference such that BC = 8 cm. What are the coordinates of point C?

(A) (10, 8)
(B) (4.4, 5.6)
(C) (2.8, 6.4)
(D) (6.4, 3.6)
(E) (3.6, 4.8)




This question is a part of Are You Up For the Challenge: 700 Level Questions collection.
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Re: Let A be (0, 0) and B be (10, 0). A semicircle is constructed with AB [#permalink]
03 Nov 2021, 07:51
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