Question

a tangent ab at a point a of a circle of radius 6 cm meets a line through center o at a point such that ob = 8 cm . find the length of ab

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

$ab=\sqrt{28}cm$

Step-by-step explanation:

From figure, oa= 6cm and ob=8cm, since ab is a tangent, therefore

oa is perpendicular to ab as the tangent at any point of the circle is perpendicular to the the radius at the point of contact.

Hence, oa⊥ab

Now, using the Pythagoras theorem,

$(Hypotenuse)^{2}=(Base)^{2}+(Perpendicular)^{2}$

$(ob)^{2}=(ab)^{2}+(oa)^{2}$

Putting the values of oa and ob in the above equation, we have

$(8)^{2}=(ab)^{2}+(6)^{2}$

$64=ab^{2}+36$

$64-36=(ab)^{2}$

$28=(ab)^{2}$

$ab=\sqrt{28}cm$

Hence, length of $ab=\sqrt{28}cm$