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

Question

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)

stne · Answer

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.

WadderBoi · Answer

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?

parasma · Answer

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.

Bunuel · Answer

This question is a part of  Are You Up For the Challenge: 700 Level Questions  collection.

KarishmaB · Answer

It is a logical question and requires no calculation. AB is the diameter with length 10 as shown so radius is 5. 
C is on the circumference such that BC is 8 which means C is somewhere as shown in the figure. Why?
BA is 10 so if C were at A, BC would be 10. As we keep moving C closer to B on the circumference, BC will become smaller and will become 8 at a point in the region shown. After all, if C were at (5, 5) then BC would be  5\sqrt{2} , which is less than 7.5. So BC would be 8 before C reaches (5, 5).

In the region where C will lie, y co-ordinate is greater than x co-ordinate but still less than 5. There is only 1 such option which is (E)

Answer (E)

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

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

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