There can be infinite tangents to a circle. A circle is made up of infinite points which are at an equal distance from a point.
Since there are infinite points on the circumference of a circle, infinite tangents can be drawn from them.
(i) A tangent to a circle intersects it in …………… point(s).
(ii) A line intersecting a circle in two points is called a ………….
(iii) A circle can have …………… parallel tangents at the most.
(iv) The common point of a tangent to a circle and the circle is called …………
(i) A tangent to a circle intersects it in one point(s).
(ii) A line intersecting a circle in two points is called a secant.
(iii)A circle can have two parallel tangents at the most.
(iv) The common point of a tangent to a circle and the circle is called the point of contact.
(A) 12 cm
(B) 13 cm
(C) 8.5 cm
(D)$\sqrt{119}$ cm
In the above figure, the line that is drawn from the center of the given circle to the tangent PQ is perpendicular to PQ.
And so, OP $\bot$ PQ
Using Pythagoras’ theorem in triangle ΔOPQ, we get,
$OQ^{2}$ = $OP^{2}+PQ^{2}$
$(12)^{2}$ =$5^{2}+PQ^{2}$
$PQ^{2}$= 144-25
$PQ^{2}$ = 119
PQ = $\sqrt{119}$ cm
So, option D, i.e., $\sqrt{119}$ cm, is the length of PQ.
In the above figure, XY and AB are two parallel lines. Line segment AB is the tangent at point C, while line segment XY is the secant.