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Triangle problem – finding height with given area and angles.

January 4, 2013 Leave a comment

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

December 16, 2011 Leave a comment

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

SOLUTION:

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Triangle – Area problem

October 31, 2011 Leave a comment

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.

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Categories: Triangles

Triangle Problem

October 8, 2011 2 comments

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.

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Triangle – Circle problem

September 30, 2011 4 comments

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 .

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An Intriguing Geometry Problem – Triangle problem

September 28, 2011 2 comments

Let ABC be an isosceles triangle (AB=AC) with BAC = 20°. Point D is on side AC such that DBC = 60°. Point E is on side AB such that ECB = 50°. Find, with proof, the measure of EDB.

For more about this question go to Berkeley Math Circle. You can read history of this question and about solutions. Picture is taken from thinkzone.wlonk.com .

SOLUTION : Read more…

Categories: Triangles