Question

In each of the following figures O is the centre of the circle find the value of x and y​

Answer 1

1) here measurement of angle formed at center of circle is is 180 deg

so measurement of angle touching circumference will be 90 deg

now it is a right angle triangle with x as hypoteneus

so

x^2 = (15)^2 + (8)^2

x^2 = 225+64

x^2 = 289

x = 17 cm answer

and x is also diameter

y = radius

so y = x/2 = 17/2 = 8.5 cm answer

2) now according a theorem

• tangents of a circle are perpendicular to its radius

so x is hypoteneus

and base = 5cm (radius)

perpendicular = 12 cm (tangent)

so x^2 = (12)^2 + (5)^2

x^2 = 144 + 25

x^2 = 169

x = 13 cm answer

now here

hypotaneus = x = 13 cm

base = 5cm

perpendicular = y cm

so

(13)^2 = (y)^2 + (5)^2

169 -25 = (y)^2

144 = (y)^2

y = 12 cm answer

which proves that tangents from a common point are equal

3) now if radius (perpendicular) = 24cm

and tangent 1 (base) = 18 cm

and hypoteneus = x cm

so

x^2 = (24)^2 + (18) ^2

x^2 = 576 + 324

x^2 = 900

x = 30 cm answer

now y will be equal to T1 (proved in question 2)

so y = 18 cm answer