Find the radius of the circle | Geometry Question | Important Geometry And Algebra Skills Explained

Find the radius of the circle | Geometry Question | Important Geometry And Algebra Skills Explained

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[elmurazbsirov]

Thank you for solving it. Hello from Baku Azerbaijan🇦🇿

[sarantiskalaitzis]

We extend BC which intersects circle in to point E and DC intersecting circle in to point F.From intersecting chords theorem we get BC•CE=CD•CF so 6•a=8•4 so CE=a=32/6=16/3.The inscribed angle ABE is right so the hypotenuse AE is diameter of circle and AE=2•r. Applying Pythag. Theorem into ABE Right Triangle AE^2=AB^2+BE^2.So (2r)^2=4^2+(6+16/3)^2 so 4•r^2=16+(34/3)^2 so 4•r^2=144/9+1156/9 so 4•r^2=1300/9 so r^2=1300/(9•4)=1300/36 hence r=(√1300)/6= 10•√13/6=5•√13/3.

[mariorossi]

Distance between chord 4 and segment 8, is 6 cm.

Taking the appropriate right triangle:
(4/2)² + (6-x)²=R²
and
(8-2)²+x²=R²
Equalling:
(4/2)² + (6-x)²=(8-2)²+x²
2²+(6²-12x+x²)=6²+x²
4=12x
x = 1/3 cm

R² = 6² + x²
R² = 36 + 1/9
R = 6, 01 cm ( Solved √ )