# 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 1 : Solution :

Using Pythagorean theorem  :

(OA)2 = (OB)2 + (AB)2

x2 = (5)2 + (12)2

x2 = 25 + 144

x2 = 169

x = 13

So, the value of x is13 cm.

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 :

0.9063 = x/20

x = 0.9063 × 20

x = 18.126

So, the missing side is 18.126 cm.

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