Geometry Practice Test 4

Question : 11 of 40

Marks: +1, -0

Let PAB be as secant to a circle intersecting at points A and B and PC is a tangent. Which one of the following is correct?

The area of rectangle with PA, PB as sides is equal to the area of the square with PC as side.
The area of a rectangle with PA, PC as sides is equal to the area of a square with PB as side.
The area of a rectangle with PC, PB as sides is equal to the area of a square with PA as side.
The perimeter of a rectangle with PA, PB as sides is equal to the perimeter of a square with PC as side.

Solution:

PAB be a secant to a circle intersecting at A and B.
PC is a tangent to the circle.

PC is the side of the square.
Area of square = PC × PC =

PC^2

PA and PB are two sides of a rectangle
PA × PB
So, according to the theorem,

PC^2

= PA × PB
So, the first statement is true.

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