Hello math bugs(π) and hivers(π)
Well come to another sweet and interesting geometeic problem. We know that the bisector of angle between two sides of a triangle divides the third and opposite side of the triangle in the ratio of the two sides that conceive the angle. Using this proeprty , we gonna find PQ in the following figure.
Before heading towards solution , we gonna discuss the axioms, postulate or the properties that we need here to solve it.
1οΈβ£ Pythagoras' theorem. Check details.
2οΈβ£ An angle bisector and how it divides the third side of a triangle.π
3οΈβ£ We also gonna need to solve a simple equation. We will check it in the end.
Solution:
First, we have to cosider βABD to find value of BD. Check the following figure:π
As we already find BD, CD will be BC - BD = (14 - 5) cm = 9 cm
π We must have very familiar to rario and its operation. For example if you are asked to divide $50 between A and B in the ratio 3 : 2, you can easily do it. A will get $30 and B will get $20. We will use the same operation to get AQ, DQ, AP and DP.
Now we can find the value of AQ and DQ. Whicn can be driven in the following way.π
Again we can find the same way the values of AP and DP. Check it below:π
π We are now at the bottom line. We just need to solve a simple equation to find the value of PQ. Check AD can be written as sum of AP and DP and again it can be written as sum of AQ and DQ. So, we got here a simple equation.
That is given by (AP + DP) = (AQ + DQ). Now check the following figure for the final touch.π
πIf you have good command over ratio and its operation, the problem can be solved without pen and paper. But Before that we need to know pythagoren triplet as here we needed 5,12 amd 13. So without any calculation we could find the third side of βABD. And then using ratio we could reach at PQ
π’ All the figures used here are made by me using android application. The figure may not be accurate in measurement, just try considering given data only. If there is any silly mistake , please try to ignore it. Though, I tried my best to put it without any misatke.
I hope you liked my today's sweet math problem and its solution.
Thank you so much for bearing me till end.
Have a nice day.
All is well
Regards: @meta007
I remember when I knew all this, now the lack of practice for years and I have no idea @meta007. Thanks for sharing the post π±π±πͺπͺπͺ
Yeah, Without practise things are dimmed.
Thank man for stoping by.
Nice meta! Very espectcular..and colorful math concept and it's visual.β€οΈ
Thanks th for the visit and compliment
Hello dear and appreciated mathematician. Wonderful strategic and pedagogical publication. Very good step by step, coinciding with the images (very well worked and designed). It is an honor for us at Hive to have people like you, who aggrandize with quality and specialized knowledge our wonderful multiverse.
Happy day to you π€
!LUV
Hello friend @marilour
Thank you so much for your sweet greeting and kind words. It means a lot.
I try to put my best, the credit goes to passers by who encourage me to bring quality posts. I am very glad that you've liked the presentation.π
Thanks once again for stoping by.
Have a great weekend.
Greetings dear friend @meta007
My words are few before so much quality that you share with us. You have generated a style that makes you your own, unique, and therefore a reason for recognition. I have always referred that you handle with dilation the pedagogical strategies to enjoy and make understandable the apparently complicated.
Thank you very much, may you continue to be successful in Hive for a long, long time, allowing us to continue enjoying your creative productions.
Happy day to you
!LUV
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Thanks man for the visit and support.
You are welcome! I don't understand everything you publish but it looks so elegant that it's hard not to like it! Keep up the good work!
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Aha! Your words more sweet and elegant than what I publish! I got very little hive power but I can support you with a few ecency points. I gonna send you 300 of it.
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Very charming, thank you!
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