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Answers
Q1
1.) one
A tangent of a circle intersects the circle exactly in one single point.
2.)two
from a point outside a circle only two tangents can be drawn to the circle.
3.) perpendicular , contact
the tangent at any point of a circle is perpendicular to the radius through the point of contact.
4.)Two
There can be only two parallel tangents to a circle.
Q2
1.)A point P is 25 cm from the centre of a circle. The radius of the circle is 7 cm.Find the length of the tangent drawn from P to the circle is
ANS:- 24cm
Given- O is the centre of a circle to which a tangent PT=x has been drawn to the circle at T when OP=25cm. The radius of the given circle=7cm
To find out: x=?
Solution- We join OT.
∴OT is a radius of the circle through the point of contact T of the tangent PT. We know that the radius through the point of contact of a tangent to a circle is perpendicular to the tangent.
∴OT⊥PT⟹∠OTP=90
o
.
∴ΔOTP is a right one with OP as hypotenuse. So, applying Pythagoras theorem, we get
PT=
OP
2
−OT
2
=
25
2
−7
2
cm=24cm.
∴ The tangent to the given circle PT=24cm.