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Help please this dued yesterday im late please help me with this question its only one!!!

Help please this dued yesterday im late please help me with this question its only-example-1

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Answer:

Explanation:

Let O be the center of the circle, and let x be the length of the radius of the circle. Since segment DE is a minor arc, it subtends an angle of less than 180 degrees at the center of the circle, and its length is given by:

length of DE = (angle AOB / 360) * 2 * pi * x

We are given that the length of DE is 52 cm, and we know that angle AOB is 2 times angle ACB, since these angles subtend the same arc. Therefore, we have:

angle AOB = 2 * angle ACB

We can use the law of cosines to find angle ACB:

cos(ACB) = (AB^2 + BC^2 - AC^2)/(2 * AB * BC)

cos(ACB) = (25 + 64 - 81)/(2 * 5 * 8)

cos(ACB) = -1/8

Since angle ACB is acute, we have:

ACB = arccos(-1/8)

ACB = 100.14 degrees (rounded to two decimal places)

Therefore, angle AOB is twice this angle, or:

angle AOB = 200.28 degrees

Substituting the values of (angle AOB, x) into the equation for the length of DE, we get:

52 = (200.28 / 360) * 2 * pi * x

Simplifying and solving for x, we get:

x = 26 / pi

The circumference of the circle is given by:

circumference = 2 * pi * x

Substituting the value of x, we get:

circumference = 2 * pi * (26 / pi) = 52 cm

Therefore, the circumference of circle F is 52 cm.

User Tashi
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