Question

Prove that the circles described on the four sides of a rhombus as diameters, pass through the point of intersection of its diagonals.

Answer 1

To prove : The circles described on the four sides of a rhombus as diameters, pass through the point of intersection of its diagonals.

Solution :

Let ABCD be a rhombus such that its diagonals AC and BD intersects at O. Let E be the centre of the circle with diameter AB.  

We know that, the diagonals of a rhombus intersect each other at a right angle (90°).

∴ ∠AOB = ∠BOC = ∠COD = ∠DOA = 90°

Now,

∠AOB = 90°  

Circle with AB as diameter will pass through centre O.

Similarly, all the circles will also described on BC, AD and CD as diameter pass through centre O.

HOPE THIS ANSWER WILL HELP YOU…..

 

Some questions of this chapter :

In Fig. 16.197, AOC is a diameter if the circle and arc AXB= 1/2 arc BYC. Find ∠BOC.

https://brainly.in/question/15910514

 

In Fig. 16.199, AB is a diameter of the circle such that ∠A=35° and ∠Q=25°, find ∠PBR.

https://brainly.in/question/15910508