Frequently Asked Questions on Chapter 10 – Circles
How many tangents can a circle have?
There can be infinite tangents to a circle. A circle is made up of infinite points which are in a equal distance from a point. Since there are infinite points on the circumference of a circle, infinite tangents can be drawn from them.
Fill in the blanks:A tangent to a circle intersects it in …………… point(s). A line intersecting a circle in two points is called a ………….A circle can have …………… parallel tangents at the most. The common point of a tangent to a circle and the circle is called …………?
A tangent to a circle intersects it in one point(s).A line intersecting a circle in two points is called a secant.A circle can have two parallel tangents at the most.The common point of a tangent to a circle and the circle is called the point of contact.
In a circle, how many tangents can be formed?
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.
Find the Length of PQ if a tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm.
Let us consider, the line that is drawn from the centre of the given circle to the tangent PQ is perpendicular to PQ.
And so, OP ⊥ PQ
By using Pythagorean theorem in triangle ΔOPQ we get,
OQ^2 = OP^2 + PQ^2
(12)2 = 52 + PQ2
PQ2 = 144 – 25
PQ2 = 119
PQ = √119 cm
Hence, the length of PQ is √119 cm.