Q29 of 805 Page 1

Prove that the tangents at any point of a circle is perpendicular to the radius through the point of contact.


In the given figure, AB is a tangent at point of contact C


D is an arbitrary point on tangent AB. Connect O with D and


E be the point on line OD on circle.


OE < OD


OC < OD (because OE and OC is radius)


So, we can say that every line from centre of circle to


tanget is greater than radius at point of contact. It means


that radius is shortest line that touches the tangent.


And we know that shortest line is always perpendicular.


So, OC AB


More from this chapter

All 805 →
27

From the top of vertical tower, the angle of depression of two cars, in the same straight line with the base of the tower, at an instant are found to be 45° and 60°. If the cars are 100 m apart and are on the same side of the tower, find the height of the tower. [Use = 1.73]

 28

Two dice are rolled once. Find the probability of getting such numbers on two dice, whose product is 12.

OR


A box contains 80 discs which are numbered from 1 to 80. If one disc is drawn at random from the box, find the probability that it bears a perfect square number.


 30

The first and last terms of an A.P. are 8 and 350 respectively. If it’s common difference is 9, how many terms are there and what is their sum?

OR


How many multiple of 4 lie between 10 and 250? Also find their sum.


 31

A train travels 180 km at a uniform speed. If the speed had been 9 km/hour more, it would have taken 1 hour less for the same journey. Find the speed of the train.

OR


Find the roots of the equation .