Complete the following proof.

given: ab is the diameter of circle o
ac and bd are tangents

prove: ac || bd

A tangent to a circle is a line intersecting the circle at exactly one point which is called point of tangency or tangency point. Also, radius from the center of the circle to the point of tangency is always perpendicular to the tangent line.

Here, O is the center of the circle and B is the point on the circumference of the circle,

⇒ OB is the radius of the given circle,

Also, BD is the tangent line for which B is the tangency point,

⇒ OB ⊥ BD ⇒ AB ⊥ BD ( Because, AOB is a straight line )

Similarly,

AB ⊥ AC

Since, if two lines are perpendicular to the same line then they are parallel to each other,

⇒ AC ║ BD

Hence, proved.

Answer is below.

Step-by-step explanation:

AB is the diameter of circle O, AC and BD are tangents - Given

AB ⊥ AC , AB ⊥ BD - Radius ⊥ to tangent

AC || BD - 2 lines ⊥ to the same line are ||

Hope this helps.

  y= -3x is the required function.

step-by-step explanation:

we have been given a table:

x             y

0             0

1             -3

3             -9

-2             6

we can see that the values of y is -3 times the value of x

hence, the function would be: y= -3x.

put the values of x will give the same y as in the table that means function is satisfying the given table.