Problem on right angle triangle and sem-circle inside.

avatar

Hello maths bugs(🐞) and hivers(🐝)
I hope you are strong and stout and doing great in life.

Today I have come up with a problem based on a right angle triangle and a semi-circle inside as shown in the figure below. We have to find out radius of it.

We have given two side of the right angle triangle. We can easily find out the 3rd side or the hypotenuse of the triangle. Check details in the below:

Details and short cut of Pythagorean triplet.

METHOD 1:

We need to copy the right angle triangle.Consider BC as axis, we need to rotate the triangle anti-clock wise and thus we find the following figure. You can see the circle (⭕) inside the triangle and touching every side of the triangle. For in-circle we know the relation between radius(r) of the circle and area () & semi peri-meter (s) of the triangle. It is given by ∆= r.s. We can also find out the area of the right angle triangle using 1/2× base× height formula.
Now equation both the formula, we can easily find the required radius(r) as you can see in the figure above. So the in-radius(r) is 3/2 cm.

For more information tap In-circle.

METHOD 2:

Let's do this using similarity.For that we have join DE which is in-radius (r). Now we get two similiar triangles. Namely ∆ABC and ∆EDC. Angle C is common for both of them and angle ABC & angle CDE equal to 90°. So ∆ABC ~ ∆EDC. From similarity we can have AC/AB equals to CD/DE or 5/3= (4-r)/r. That seams 5r =12 - 3r or 8r = 12 or r= 3/2.

For similarity and how to use it,tap similarity please.

Please ignore the mistakes if you can. Make a comment if you have suggestion or if you need further detailing about the topic or if you want more of this kind of tricky problem.I will be glad to reply you.

Thanks for visiting and supporting. It means a lot.

Have a nice day.

All is well.

Regards: @meta007



0
0
0.000
14 comments
avatar

How interesting that there is a publication with mathematical procedures, continue with more content so someone who really likes mathematics tells you

0
0
0.000
avatar

Thank you so much esteva for visiting and appreciating.

0
0
0.000
avatar

Congratulations @meta007! You have completed the following achievement on the Hive blockchain and have been rewarded with new badge(s):

You published more than 30 posts.
Your next target is to reach 40 posts.

You can view your badges on your board and compare yourself to others in the Ranking
If you no longer want to receive notifications, reply to this comment with the word STOP

To support your work, I also upvoted your post!

Support the HiveBuzz project. Vote for our proposal!
0
0
0.000
avatar

My Head is Spinning after seeing These Triangles or Math 🤣🤣🤣 !PIZZA

0
0
0.000
avatar

🤣🤣 spinning ..hahah.How long out of math dude? Long gap in practise can feel you so. It's okay man.Thanks for visiting.

0
0
0.000
avatar
(Edited)

🍕 PIZZA !

I gifted $PIZZA slices here:
idksamad78699 tipped meta007 (x1)
@blitzzzz(14/20) tipped @meta007 (x1)

Send $PIZZA tips in Discord via tip.cc!

0
0
0.000
avatar

This post has been manually curated by @bhattg from Indiaunited community. Join us on our Discord Server.

Do you know that you can earn a passive income by delegating to @indiaunited. We share 100 % of the curation rewards with the delegators.

Here are some handy links for delegations: 100HP, 250HP, 500HP, 1000HP.

Read our latest announcement post to get more information.

image.png

Please contribute to the community by upvoting this comment and posts made by @indiaunited.

0
0
0.000
avatar

Another great explanation of a Math problem 💯 !PIZZA 🍕

0
0
0.000
avatar

I am glad that you liked it.😄😄
Thanks for stopping by.

0
0
0.000
avatar

Thanks for your contribution to the STEMsocial community. Feel free to join us on discord to get to know the rest of us!

Please consider delegating to the @stemsocial account (85% of the curation rewards are returned).

Thanks for including @stemsocial as a beneficiary, which gives you stronger support. 
 

0
0
0.000
avatar

Mathematic is perfect but diffucult :(

0
0
0.000
avatar

😄😳 You are somewhat right.

Thanks for visiting man.

0
0
0.000