Question

O. A Tangent pa at point p of airch of radius 5 ang
and muts a line through contre o at a, such that
og is a 8 12 . Find the length.​

Answer 1

Step-by-step explanation:

Given-

O is the center of a circle of radius 5cm,

PQ is a tangent to the given circle at P.

PQ meets the line OP passing through O & P.

OQ=12cm.

To find out- PQ

Solution-

We join OP.

Then OP is a radius of the given circle through the point of contact P of the tangent QP.

∴OP⊥QP

i.e ∠OPQ=90

o

....The angle between a tangent and the radius through the point of contact is 90

o

∴ΔOPQ is a right one with OQ as the hypotenuse.

So, applying Pythagoras theorem, we have

PQ=

OQ

2

−OP

2

=

12

2

−5

2

cm=

119

cm.