Here is a right angled triangle work out the value of x using trigonometry
1 answer:
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Option A
Length of CD is 10 inches
<u><em>Solution:</em></u>
The diagram is attached below
Given that, Circle A and circle B are congruent
CD is a cord of both circles
AB = 24 inches
Radius = 13 inches
To find: length of CD
Draw a straight line connecting A and C
AC represents the radius of circle. Also given that radius is 13 inches, So AC = 13 inches
Given in question that AB = 24 inches
Therefore from figure, AO = AB/2 = 24/2 = 12
AO = 12
Let "b" be the length of CO
Therefore, CD = CO + OD = b + b
AOC forms a triangle, so we can use pythogoras theorem
Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.
By above definition for triangle AOC
Substituting AC = 13 and AO = 12 and OC = b
<em><u>Thus length of CD is:</u></em>
CD = b + b = 5 + 5 = 10
Thus length of CD is 10 inches
Answer:
(x - 6)² + (y - 2)² = 128
Step-by-step explanation:
Given as the circle has center ( 6 , 2)
and it passes through points (-2 , -6)
Now , standard equation of circle is (x -a)² + (y- b)² = r² , where (a , b) is center and r is the radius .
Again from given center the circle equation is
(x- 6)² + (y- 2)² = r²
Now this circle passes through points (-2 , -6)
so, (-2 -6)² + (-6 -2)² = r²
so, 8² + 8² = r²
Or, 128 = r²
i.e Radius pf this circle = 8
Hence the circle equation formed is
(x- 6)² +( y-2)² = 128 Answer