Q33 of 40 Page 1

Prove that the parallelogram circumscribing a circle is a rhombus.

Consider a parallel gram ABCD circumscribing a circle with center O.


To Prove: ABCD is a rhombus or AB = BC = CD = AD


We know, tangents from an external point to a circle are equal


AP = AS


BP = BQ


DR = DS


CR + CQ


Adding above equations, we get


AP + BP + CR + DR = AS + DS + BQ + CQ


AB + CD = AD + BC


Now, In a parallelogram AB = CD and BC = AD





Hence, Proved!


More from this chapter

All 40 →
31

Determine graphically the coordinates of the vertices of a triangle, the equations of whose sides are given by 2 y-x=8,5 y-x=14 and y-2 x=1

OR


If 4 is a zero of the cubic polynomial x3-3 x2-10 x+24, find its other two zeroes.


 32

A train covers a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. Find the original speed of the train.

 34

Prove that : 2(sin6 θ +cos6 θ )-3(sin4 θ + cos4 θ) + 1= 0.

 35

The following table gives production yield per hectare (in quintals) of wheat of 100 farms of a village :

Change the distribution to 'a more than' type distribution and draw its ogive.


OR


The median of the following data is 525. Find the values of x and y, if total