Question

Complete the following proof.

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

Prove: AC || BD

Answer 1

Answer is below.

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.

Answer 2

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.