Chapter 15, Problem 4CR

To determine

To Find: Distance from the center of the circle and the chord.

Answer to Problem 4CR

  $5$

Explanation of Solution

Given:

  $\begin{array}{l}\text{Diameter}=26\\ \text{Chord Length}=24\end{array}$

Formula Used:

  $\text{Pythagoras Theorem}:h^2=b^2+p^2$

Calculation:

  

  $\begin{array}{l}Let,AB=26\\ CD=24\\ radii=\frac{AB}{2}=AO=OB=OD=OC=13\\ DE=EC=12\\ O{D}^2=D{E}^2+O{E}^2\\ \text{⇒}{13}^2=O{E}^2+{12}^2\\ \text{⇒}O{E}^2=169-144\\ \text{⇒}OE=\sqrt{25}=5\end{array}$

Conclusion:

Thus the required distance between center and the chord is $5$ .