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sqdancefan
The angle the radius makes with AB is a right angle, so the Pythagorean theorem applies.
  r² = 17.4² - 7² = 253.76
  r = √253.76 ≈ 15.9

The length of radius r is about 15.9.

The radius of the circle is 15.9

What is nearest tenth ?

nearest tenth means to write the given decimal number up to one decimal place

How to find the length of radius?

The centre of circle is O. AB is the tangent to the circle at B.

OB is the radius.

Let OB = r

  • The tangent to the circle is perpendicular to the radius of the circle at the point of contact.
  • Here, AB ⊥ OB
  • Δ OAB is right angled triangle, where AO is the hypotenuse.

By using Pythagorean theorem,

[tex]r^{2} =(AO)^{2} -(AB)^{2}[/tex]

⇒ [tex]r^{2}=(17.4)^{2} -7^{2}[/tex]

⇒ r= √253.76 = 15.9

∴ The radius of the circle is 15.9

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