Question

Help to this explanation , this is a review practice.

Answer 1

To solve this problem we will use the Pythagorean theorem twice:

`c^2=a^2+b^2,`

where c is the length of the hypotenuse and, a, and b are the lengths of the legs.

Now, from the triangle OPD, we get ( we will omit the units to simplify the calculations):

`OP^2=1.2^2+OD^2.`

Notice that OD is a radius of the circle, therefore OD=1, and OP=OC+CP=1+CP, then we can rewrite the above equation as:

`\begin{gathered} 1+CP=√(1.2^2+1^2), \\ CP=\sqrt{(11)/(5)}-1\approx0.56. \end{gathered}`

Analogously, we get that:

`\begin{gathered} AP^2=AD^2+1.2^2=2^2+1.2^2, \\ AB+BP=1.7+BP=√(4+1.2^2), \\ BP=√(4+1.2^2)-1.7\approx0.63. \end{gathered}`

Therefore,

`\begin{gathered} Distance(P,C)\approx0.56\text{ }in, \\ Distance(P,B)\approx0.63\text{ in.} \end{gathered}`

Answer:

`Point\text{ C.}`