Math Is Fun Forum

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Incircles, triangles and iffy conjectures.

Hi;

This problem appeared in another thread.

a triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6cm respectively. find the sides AB and AC.

Everyone stresses how you should always make a drawing. Teachers, mathematicians, physicists, scientists, engineers,  forum people... It is funny to watch people trying to draw circles, triangles and tangents freehand. The circles look like ellipses, the triangles have rounded sides and the tangents often miss the circle completely.

Why not make an accurate drawing instead? Geogebra to the forefront!

The drawing below takes about 10 minutes and does not show any particular brilliance just some dexterity with the mouse and my 93 year old fingers.

Immediately we see that AB is very likely 15.  We also see we can now apply the following idea:

Suppose the tangency points of the incircle divide the sides into lengths of x and y, y and z, and z and x. Then the incircle has the radius

We say x = 8, y =6 and r = 4 then we solve for z. We get z is 7. Then 8 + 7 = 15 and we are done with our iffy conjecture.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Incircles, triangles and iffy conjectures.

hi bobbym,

I've now fleshed out my method from the other thread:

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Incircles, triangles and iffy conjectures.

H bob bundy;

That looks okay to me. Very good!

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.