Q6 of 105 Page 598

In the given figure, PT is a tangent to the circle with center O. If OT = 6 cm and OP = 10 cm, then the length of tangent PT is

We have given, PT is a tangent drawn at point T on the circle.


∴ OT ⏊ TP


[Tangents drawn at a point on circle is perpendicular to the radius through point of contact]


So, In △OTP we have,


By Pythagoras Theorem,


[i.e. (Hypotenuse)2 = (Base)2 + (Perpendicular)2]


(OP)2 = (OT)2 + (PT)2


(10)2 = (6)2 + (PT)2


(PT)2 = 100 - 36


(PT)2 = 64


⇒ PT = 8 cm

More from this chapter

All 105 →
4

Which of the following pairs of lines in a circle cannot be parallel?

 5

The chord of a circle of radius 10 cm subtends a right angle at its center. The length of the chord (in cm) is

 7

In the given figure, point P is 26 cm away from the center 0 of a circle and the length PT of the tangent drawn from P to the circle is 24 cm. Then, the radius of the circle is

 8

PQ is a tangent to a circle with center O at the point P. If ΔOPQ is an isosceles triangle, then ∠OQP is equal to