A geometry problem by Chung Kevin

Geometry Level 3

In triangle $ABC$ , $AB = 6$ .
$D$ is a point on $AC$ such that $AD = BD = CD = 5$ .
What is the length $BC$ ?

The answer is 8.00.

1 solution

Sharky Kesa
Jan 6, 2017

Since $D$ is equidistant from $A$ , $B$ and $C$ , so $D$ is the circumcenter of $ABC$ . Also, since $D$ is the midpoint of $AC$ , $AC$ must be a diameter of the circumcircle, so $\angle ABC = 90^{\circ}$ . Thus, $ABC$ is a right triangle. Note that $AB=6$ and $AC=10$ . Thus, by Pythagoras theorem , $BC = \sqrt{10^2 - 6^2} = \boxed8$ .

I was trying to hide the fact that "In a right triangle, the circumcenter is the midpoint of the hypotenuse".

Chung Kevin - 4 years, 5 months ago

For that you could have used some numbers which are not pythagorean triples. That will allow people(some people) to doubt(but not for much time). Well the thing which you were thinking to hide is the ultimate truth. LOL

Vishwash Kumar ΓΞΩ - 4 years, 5 months ago

A geometry problem by Chung Kevin

The answer is 8.00.

1 solution

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