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Explanation:
Chords EF and HG are the same length (16 units). This means that they are the same distance away from the center point Q.
Based on that we know segments QA and QB are the same length.
Let's find x.
QA = QB
7x-6 = 4x+3
7x-4x = 3+6
3x = 9
x = 9/3
x = 3
From that we can find...
Both segments are 15 units each to confirm we have the correct x value.
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Now draw a segment from point Q to point G.
This forms right triangle QBG.
The leg BG is half of chord HG, so BG = 0.5*16 = 8 units
We just found QB and it is 15 units.
Use the pythagorean theorem to find the hypotenuse QG
a^2 + b^2 = c^2
(BG)^2 + (QB)^2 = (QG)^2
8^2 + 15^2 = (QG)^2
289 = (QG)^2
(QG)^2 = 289
QG = sqrt(289)
QG = 17 is the radius
Answer: 21.9 units
Step-by-step explanation:
Each right angle indicates that a right triangle is formed due to geometry theorems.
In short, below are the steps to take to solve this problem:
1) You have to note that each pair with the bisectors can form a right angle triangle. After that, you can use Pythogoreas' theorem to solve finally for radius of Q.
2)
4²+ (4x+3)²= (7x-6)²+4²
(4x+3)= (7x-6)
x=3
4x+3=15
15²+16²=r²
r=21.9 units
