1. Fill in the blanks:
(i) The common point of tangent and the circle is called _________.
Soln: point of contact.
(ii) A circle may have _____ parallel tangent.
Soln : two
(iii) A tangent to a circle intersects it in ______ point.
(iv) A line intersecting a circle in two points is called a _______
(v) The angle between tangent at a point P on circle and radius through the point is _______
Q 2. How many tangents can a circle have?
Tangent: a line intersecting circle in one point is called a tangent
As there are infinite number of points on the circle , a circle has many ( infinite ) tangents.
Q 3. ‘O’ is the centre the circle shown below with a radius of 8 cm. The circle cuts the tangent AB through O at B such that AB = 15 cm. Find OB.
Given data : AB = 15 cm
OA = 8 cm ( radius of the circle )
We know that : the tangent cuts the circle at 90 degrees. Therefore, OA is the hypotenuse of the triangle OAB . Hence, the longest side can be found by using pythagoras Theorem.
OB = 17 cm
Therefore, OB = 17 cm
Q 4. If the tangent at point P to the circle with centre O cuts a line through O at Q such that PQ = 24 cm and OQ = 25 cm . find the radius of the circle.
PQ = 24 cm
OQ = 25 cm
OP = radius = ?
P is a point of contact , at point of contact , tangent and radius are perpendicular to each other.
Therefore triangle is right angled triangle angle OPQ = 90°
BY pythagoras theorem,
OP = 7 cm
Therefore , OP = radius = 7 cm