Chapter 10.3, Problem 1MRE

To determine

To calculate: AB

Answer to Problem 1MRE

  $AB=12$

Explanation of Solution

Given information: Radius of a circle is equal to 5 and $AO=13$

Calculation:

  

A tangent to a circle is a line that intersects the circle at just one point.

At point B, AB is tangential to circle.

OB is the radius

  $OB\perp AB$ (In a circle, radius is orthogonal to the tangent)

In $\Delta ABO$ ,

  $A{O}^2=A{B}^2+B{O}^2$

(In a right-angled triangle, sum of squares of thetwo sides is equal to the square of hypotenuse)

Put $AO=13,OB=5$

  $\begin{array}{l}{13}^2=A{B}^2+5^2\\ \Rightarrow 169=A{B}^2+25\\ \Rightarrow A{B}^2=169-25=144\\ \Rightarrow AB=\sqrt{144}=12\end{array}$