Magic Of Mid-Point!

Geometry Level pending

$ABC$ is an acute angled triangle with angle $B = 30^{o}$ , $H$ is orthocenter and $M$ is the midpoint of $BC$ . On the line $HM$ a point $T$ is taken such that $HM = TM$ . If $AT = 8$ , find the length of $AC$ .

The answer is 4.

1 solution

A Former Brilliant Member
Jul 30, 2020

The point $T$ lies on the circumcircle of $\triangle {ABC}$ , and is diametrically opposite to the vertex $A$ .

So, $|\overline {AT}|=2R=8$ , where $R$ is the radius of the circumcircle of the triangle.

Therefore $|\overline {AC}|=8\sin 30\degree=\boxed 4$ .

Can you please share its diagram? Thanks!

Mahdi Raza - 10 months, 1 week ago

Magic Of Mid-Point!

The answer is 4.

1 solution

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