1 answer

A triangle has corners at #(2 , 6 )#, #(4 ,8 )#, and #(1 ,5 )#. What is the radius

Question:

A triangle has corners at #(2 , 6 )#, #(4 ,8 )#, and #(1 ,5 )#. What is the radius of the triangle's inscribed circle?

Answers

Inradius doesn't exist, as the pts. are col-linear.

Explanation:

Observe that, for all the given pts., the foloowing relation holds :--

ordinate (i.e., y co-ordinate) = abscissa (i.e., x co-ordinate) +4.

This means that they are col-linear pts., all lying on the line #y=x+4.#

Hence, no triangle can be formed, & as such, inradius can not be found.

Collinearity of the given pts. can also be established as under:-

Let the given pts. be #A(2,6),B(4,8),C(1,5).#

Then Dist.

#AB#=#sqrt{(2-4)^2+(6-8)^2}=2sqrt2.#
Dist.#BC#=#sqrt{(4-1)^2+(8-5)^2}=3sqrt2.#
Dist.#CA#=#sqrt{(2-1)^2+(6-5)^2}=sqrt2.#

We find that, #AB+CA=BC, # proving the collinearity.

.

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