Hello math bugs(🐞) and hivers(🐝)

I hope you are strong and stout and doing great in life.

Once again I am back with another geometric problem.To prepare all the figures and and solution I did my best.You must have seen the problem in the cover photo.Check the problem once again and try to solve the it. Then step forward to the solution.

I have seen people have less interest to find solution.My moto is to convince them visualising the problem. That's why I always makes the figure colourful.If people do not like my work, hard work will be worthless. Let's see how people react to the article.

**The first step** is to draw a line as you can see it below in white color and thus the quadrilateral ADOE gets divided into two part i.e ∆ADO and ∆AEO. Let the area of ∆ADO and ∆AEO be **a** cm and **b** cm respectively.

**The concept I am going to use as follows:**

We know that the area of a ∆ depends on two things i.e the height and the base of a given ∆. The beauty of the concept is when height (perpendicular distance) equals, the ratio of bases becomes the ratio of area of the triangles.Check it in the figure below:

**In the above figure raito of the sides BD & AD is equal to the ratio of area of ∆BDC & ∆ADC respectively.**

**The figure below contains the same element while the triangle are ∆CBE and ∆ABE.**

**Solution as follows**:

You can see two equation in the figure below.Both of them are made using the concept I mentioned in previous figure or in point.**In the first equation** ratio of AD & BD equals to the ratio of area of ∆ADC & ∆BDC. And **in the second equation** the same thing is done considering ∆AOC & ∆ABC.You can check it in the figure below as words may confused you.😂

**I solved the problem using just triangle property.
There are others ways also to solve it**.

let's say mass point geometry. This concept can make it easier but many may not aware of it so I avoided it.If you want to know mass point geometry for a easier solution, make a comment right below the post.

**Time for visualising our answer below:**

**Some links of my previous articles you may like them**

Problem on angle bisectors of a ∆

I hope you liked today's problem and the solution.

Thank you for so much for visiting.

Have a nice day

All is well

**Regards:** @meta007