Chapter 10.8, Problem 4PSA

a)

To determine

To Find: Find TR

Answer to Problem 4PSA

  $TR=50$

Explanation of Solution

Given Information:$\begin{array}{l}\text{1) T is midpoint of }QS\\ \text{2) PT = 8}\\ \text{3) QS = 40}\end{array}$

Formula Used:

1) If two chords intersect inside a circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

Calculation:

  $\begin{array}{l}\text{Let}OT\text{ be }x\\ O{S}^2=O{T}^2+T{S}^2\\ $ {(x+8)}^2=x^2+{20}^2$x^2+16x+64=100+x^2\\ 16x=336\\ x=21\\ PO=PT+TO\\ OP=8+21\\ OP=29\end{array}$

b)

To determine

To Find: Find diameter of circle

Answer to Problem 4PSA

  $\text{Diameter}=58$

Explanation of Solution

Given Information:$\begin{array}{l}\text{1) T is midpoint of }QS\\ \text{2) PT = 8}\\ \text{3) QS = 40}\end{array}$

Formula Used:

1) If two chords intersect inside a circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

2) ythagoras Theorem

Calculation: $\text{ Diameter = }2\cdot OP=2\cdot 18=58$