mangamma 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)
Look at the figure below, It's a Right angled triangle.
Property:
The triangle ABC inscribes within a semicircle. The angle at vertex C is always a right angle of 90°, and therefore the inscribed triangle is always a right angled triangle providing points A, and B are across the diameter of the circle.
We know two sides. AB= 10, and BC=8 so using Pythagoras theorem AC=6
So we need to find the distance from the Vertex C to the origin.
Let the Coordinates of C be X and Y then
C=(X,Y)
\(\sqrt{(X-0)^2+(Y-0)^2}\)= 6
\(\sqrt{(X)^2+(Y)^2}\)=6
\((X)^2+(Y)^2\)=36
Looking at the answer choices, two positive numbers when squared and added should be 36, we can straight away reject options A,C and D as squaring them itself comes to more than 36. It's between B and E, a little trial shows the answer is E.
\(3.6^2 +4.8^2\) =36
\(\sqrt{3.6^2 +4.8^2}\)=6
C =( 3.6,4.8)
Answer E
Hope this is helpful.
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