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CB is tangent to ⊙A at point C. Find the radius. CB ⊥ AC by the radius-tangent theorem, so ∠C is a right angle. ΔABC is a right triangle, so apply the Pythagorean theorem. Use the steps and solve for the radius. r2 + 82 = (r + 5)2 r2 + 64 = r2 + 10r + 25 r =

Respuesta :

r2 + 82 = (r + 5)2
r2 + 64 = r2 + 10r + 25

r = 39/10

Answer:

r=3.9

Step-by-step explanation:

Given that CB is a tangent to circle with point of contact at C

Centre is at A

Hence AC is perpendicular to CB or ABC is a right triangle with hypotenuse as AC

AC = r

AB=r+5

BC=8

By Pythagorean theorem,

[tex]r^2+8^2=(r+5)^2\\r^2+64=r^2+10r+25\\10r =64-25=39\\r=39/10 =3.9[/tex]

r=3.9

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