Chapter 8.5, Problem 9PSA

Solution

To Calculate: Measures of PO and JP.

Measures of PO and JP are $\frac{5}{2}$ and $2$ respectively.

Given information: $\angle J\cong \angle MKO,MK=12,KO=8,MO=10,JK=3$ is provided in question which will help to find the solution.

Formula used: Here, we are using Angle Angle similarity.

Calculation: In $\Delta KMO$ and $\Delta JMP$

  $\angle M=\angle M$ (common)

  $\angle KJP=\angle MKO$ (corresponding angles)

Hence, $\Delta KMO\sim \Delta JMP$ (by Angle Angle similarity)

So, $\frac{MK}{JK}=\frac{KO}{JP}$

Now, putting the values

➔ $\frac{12}{3}=\frac{8}{JP}$

➔ $JP=2$

And, also $\frac{MO}{OP}=\frac{OK}{JP}$

Now, putting the values

➔ $\frac{10}{OP}=\frac{8}{2}$

➔ $OP=\frac{5}{2}$