DISTANCE BETWEEN IN-CENTRE AND CIR-CUM-CENTRE.
hive-163521·@meta007·
0.000 HBDDISTANCE BETWEEN IN-CENTRE AND CIR-CUM-CENTRE.
Hello math bugs(🐞) & hivers(🐝) I hope you are strong and stout and doing well. Today the question is finding **distance between In-centre and Cir-cum-centre**.Check the following the following figure and try to find out the solution.You need to every inch and out of In-circle and cir-cum-circle and their relation to solve it.  **The distance between two above mention centres represents by :**d = √(R²-2rR) Where **R** represents Cir-Cum-Radius and **r** represents In-Radius. **It is time to prove.It may be quite complicated but give it a try.** **Need to know three things:** 📯When the line joining In-centre and the vertices is produced to Circumference of the Cir-cum-circle, what we get check below:When we try proving something in geometry, we should know related proven staff.So I am not proving it here.🤪 I'll keep it for some other day otherwise it will be very irritating to get all the things at the same time. 📯📯As **AI** in the figure is angle bisector so angle A get divided into **a** And thus angle B to **b** each.Again angle BIQ becomes **(a+b)** as external angle of a triangle is equals to sum of internal opposite angle of a ∆.So we have **BQ=IQ.Check details below:** 📯📯📯The two pink and red triangles are similiar because they have two equal angles.Find it in the following figure: **So what we get is in the following figure and also coming to the proof.Bang! Bang! here it is:****We can proof the formulla using sine rule and cosine rule also but before that I had to prove them also.If used that method it would be more complicated. So I decided use geometry.** The In-radius is perpendicular drawn form the centre to the sides of the triangle and the Cir-Cum-Radius is distance between vertices and Cir-cum-centre. So the solution is given below. **The construction may be in appropriate because it is done without taking measurement (what eye sight tells).** ✅ Check previous related post below: [In-Centre](https://ecency.com/hive-163521/@meta007/knowing-in-circle) [Cir-Cum-Cirlce](https://ecency.com/hive-163521/@meta007/knowing-cir-cum-circle) I hope you enjoyed giving a little bit trouble to your brain.Thank you so much for visiting. Have a great day All is well Regards: @meta007
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