FIND THE VALUE OF X GIVEN A TANGENT TO A CIRCLE

Calculate the length of sides labelled in the circles below. The lines AB and AC are tangents.

Problem 2 :

Solution :

Using Pythagorean theorem  :

(AO)² = (AB)² + (OB)²

(20)² = (x)² + (8)²

400 = x² + 64

x² = 400 - 64

x² = 336

x = 18.330

So, the value of x is18.330 cm.

Problem 3 :

Solution :

Using Pythagorean theorem  :

OA² = AC² + OC²

30² = 20² + x²

900 = 400 + x²

x² = 900 - 400

x² = 500

x = 10√5

So, the value of x is 22.36 cm.

Calculate the size of x in the circles below. The lines AB and AC are tangents.

Problem 4 :

Solution :

sin x = opposite/hypotenuse

= BO/AO

= 6/13

sin x = 0.4615

x = sin ^-1 (0.4615)

= 27.48

So, the angle is 27.48.

Problem 5 :

Solution :

sin x = opposite/hypotenuse

x = AB/AO

= 12/15

sin x = 0.8

x = sin^-1 0.8

= 53.13

So, the angle is 53.13.

Problem 6 :

Solution :

cos 25^º = adjacent/hypotenuse

0.9063 = x/20

x = 0.9063 × 20

x = 18.126

So, the missing side is 18.126 cm.