Chapter 12, Problem 42CR

To determine

To find: The diameter of the pizza Clarence ate which is in the shape of a part of a circle.

Answer to Problem 42CR

The diameter of the pizza Clarence ate is 50 cm.

Explanation of Solution

Given Information:

Distance of chord from the midpoint of arc = 5 cm

Length of the chord = 30 cm

Formula used:

By Pythagoras theorem,

  ${\text{Hypotenuse}}^2={\text{Base}}^2+{\text{Altitude}}^2$

Calculation:

Let $x$ be the radius of the pizza C ate.

Draw radius $OP$ and then draw a line $\perp$ to the chord

We know that, a perpendicular from the centre of a circle to the chord bisects it.

So, $PR=\frac{30}{2}=15\text{cm}$

Now, $OR\perp PQ$

  

Here, $\Delta ORP$ forms a right triangle with $\angle ORP={90}^{\text{o}}$

By Pythagoras theorem,

  ${\text{Hypotenuse}}^2={\text{Base}}^2+{\text{Altitude}}^2$

  $\begin{array}{l}\therefore O{P}^2=P{R}^2+O{R}^2\\ \therefore x^2={15}^2+{\left(x-5\right)}^2\\ \therefore x^2=225+x^2-10x+25\\ \therefore 10x=250\\ \therefore x=25\text{cm}\end{array}$

Hence, diameter of the pizza is 50 cm.