The perimeter of angle ABC is 98 centimeters. If the radius circle A is twice the radius of circle C and the radius of circle B
is four times the radius of circle C, then find the radius of circle C.
1 answer:
Answer: Circle C has a radius of 7 cm.
Explanation:
Referring to the illustration below:
Let's denote the radius of circle C as x.
Circle A's radius can be represented as 2x.
Circle B's radius can be expressed as 4x.
The length of side AC in triangle ΔABC becomes x + 2x = 3x.
For side BC of triangle ΔABC, we get 4x + x = 5x.
Similarly, for side AB of triangle ΔABC, it is 4x + 2x = 6x.
Given that the perimeter of triangle ΔABC totals 98 cm.
Remember, the perimeter refers to the total length around the triangle.
Hence, Perimeter = 6x + 5x + 3x = 98 cm.
Thus, 14x = 98.
From this, we find x = .
Therefore, x = 7.
This concludes that the radius of circle C is 7 cm.
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Answer:
The measurement of angle HBC is m∠HBC=61°
Step-by-step explanation:
The given problem states that
The line BH divides angle EBC into two equal parts,
consult the attached diagram for clarity
thus
m∠EBC=m∠EBH+m∠HBC
where m∠EBH=m∠HBC
therefore
m∠EBC=2(m∠EBH)
Insert the provided values to solve for a
Determine the value of angle EBH
m∠EBH=(4(4)+45)=61°
Keep in mind that
m∠EBH=m∠HBC
therefore
The measurement of angle HBC is m∠HBC=61°
