### Archive

Archive for the ‘Triangles’ Category

## Triangle problem – finding height with given area and angles.

If the area of triangle ABC is ${\cal S}$ and angles $\angle A= \alpha$ and $\angle B= \beta$ then find a altitude of triangle which drawn from C to AB.

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## Triangle problem – find an angle

Triangle ABC is isosceles, AC=BC. $\angle ADE=10^\circ , \angle CBD=20^\circ .$ Find measure of angle $\angle AED$ .

SOLUTION:

Categories: Triangles Tags: , , ,

## Triangle – Area problem

In triangle ABC, cevians AD, BE and CF intersect at point P. The areas of triangles PAF, PFB, PBD and PCE are 40, 30, 35 and 84, respectively. Find the area of triangle ABC.

Categories: Triangles

## Triangle Problem

Let triangle ABC be isosceles with AB = AC. The altitude from A is AE and cevian BF intersects AE at D. If AF : AC = 1 : 3 Then find AD : DE and BD : BF.

Just draw cevian CG that intersects AE at D, too . (G is on line AB) Connect F & G. Line FG is parallel to BC. Use similarity of triangles to solve the questions.

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## Triangle problem

October 4, 2011 1 comment

Let triangle ABC be acute and let H be its orthocenter. The altitudes $AA_1 \: BB_1 \: CC_1$ . Prove that $\frac{AH}{AA_1} + \frac{BH}{BB_1} + \frac{CH}{CC_1} = 2$
It is easy question. Use areas to solve it.

Categories: Triangles Tags: , , ,

## Triangle – Circle problem

Given triangle ABC. $\angle C = 90^\circ$ . CD is height of triangle ( point D is on hypotenuse AB ). The radiuses of incircles of triangles ACD and ABD are $r_1 \: and \: r_2$ . Find the radius of incircle of triangle ABC .