Interactive step-by-step animation using GeoGebra. Post your solution in the comment box below.

Level: Mathematics Education, High School, Honors Geometry, College.

Details: Click on the figure below.

## Friday, March 6, 2020

### Geometry Problem 1457: Altitudes, Circles, Similarity, Product of the Inradii Lengths

Labels:
altitude,
circle,
GeoGebra,
inradius,
inscribed,
ipad,
ipadpro,
length,
perpendicular,
product,
similarity,
typography

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Let BC1 = BH = BA1 = p, AC1 = AH = AB1 = q and CA1 = CH = CB1 = u where I have used my proof of Problem 1456

ReplyDeleteThen r1/r4 = q/p, r3/r6 =u/q and r5/r2 = p/u

Multiplying, we get r1.r3.r5 = r2.r4.r6

Sumith Peiris

Moratuwa

Sri Lanka

https://photos.app.goo.gl/kU6aZQZw5cy48XQh9

ReplyDeleteNote that triangles AHB1 and BA1H are isosceles and similar ( case AA)

So ratio of inradius of similar triangles = ratio of altitudes => r1/r4= AHb/BHa

So r1/r4 x r3/r6 x r5/r2= 1 Per Ceva’s theorem