# Area of the Parallelogram Between Two Circles

Geometry math problem – Area of the “Parallelogram” Between two Circles, sides of the parallelogram formed by connecting the tangents of the circle. tangents are starts from two ends of a line, which is formed by diagonals of the two circles

## How to find the area of the parallelogram between two circles

From the figure, BC, BD, AE and AF are tangents, If the radius of two circles is 1 cm find the area of the blue parallelogram

## Solution

We can start from the figure

From the figure, Area of the triangle PAB = Area of the triangle QAB

Connect PO and C with the centre of the 1st circle

From triangle BCL

sin y = CL/BL

⇒ sin y = 1/3

⇒ tan y = 1/(2√2)

From triangle BOP

tan y = PO/BO

⇒ tan y = PO/2

⇒ PO/2 = 1/(2√2)

So, PO = 1/√2

Area of the triangle PAB = ½ × AB × PO

⇒ Area of the triangle PAB = ½ × 4 × (1/√2)

⇒ Area of the triangle PAB = √2 cm²

So, Area of the parallelogram = 2 × √2

⇒ **Area = 2√2 cm²**