Question

Line PD is tangent to a circle of radius 1 inch centered at O. The length of PD is 1.2 inches. The length of AB is 1.7 inches. Which point on the circle is closest to point P?

Answer 1

Point C is closest to the point P.

Explanation:

In the diagram,

The Angle between a Tangent and a radius is 90°, therefore Triangle PAD is a right triangle.

In Right Triangle PAD,

Diameter of the Circle, |AD|=2 Inch

|PD|=1.2 Inch

Using Pythagoras Theorem

|AP|²=|AD|²+|PD|²

=2²+1.2²=5.44

|AP|=√5.44=2.33Inch

|AB|+|BP|=|AP|

1.7+|BP|=2.33

|BP|=2.33-1.7=0.63 Inch

Similarly, In Right Triangle POD

Radius, |OD|=1 Inch

|PD|=1.2 Inch

Using Pythagoras Theorem

|OP|²=|PD|²+|OD|²

=1.2²+1²=2.44

|OP|=√2.44=1.56 Inch

|OC|+|CP|=|OP|

1+|CP|=1.56

|CP|=1.56-1=0.56 Inch

Since |BP|=0.63 Inch and |CP|=0.56 Inch, the point C is closest to the point P.