I will give brainliest In ⊙O, chord XY is 8 cm long and is 10 cm from O. What is the radius ⊙O?

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I will give brainliest In ⊙O, chord XY is 8 cm long and is 10 cm from O. What is the radius ⊙O?

Recall that, the closest distance from the chord to the center, is a perpendicular line to the chord, thus, check the picture below.

[tex]Circle o has radius 10. chord xy is 8 cm long. how far is the chord from the center of the circle?[/tex]

Step-by-step explanation:

perpendicular from center always bisects the chord of circle.

1/2 of chord=1/2×8=4 cm

[tex]r=\sqrt{4^2+10^2} =\sqrt{16+100} =\sqrt{116} \approx 10.77 ~cm[/tex]

radius ≈ 10.77 cm

Step-by-step explanation:

The segment from the centre O to the chord is a perpendicular bisector.

Thus 2 right triangles are formed with legs 10 cm and 4 cm ( half of XY )

The radius r is the hypotenuse.

Using Pythagoras' identity, then

r² = 4² + 10² = 16 + 100 = 116 ( take the square root of both sides )

r = [tex]\sqrt{116}[/tex] ≈ 10.77 cm ( to 2 dec. places )