## Quadrilateral Problem

In quadrilateral ABCD with diagonals BD and CA, Read more…

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

If the area of triangle ABC is and angles and then find a altitude of triangle which drawn from C to AB.

**HINT:** Read more…

## Triangle problem – find an angle

## Triangle – Area problem

In triangle * ABC*, cevians

**,**

*AD***and**

*BE***intersect at point**

*CF***. The areas of triangles**

*P***,**

*PAF***,**

*PFB***and**

*PBD***are**

*PCE***,**

*40***,**

*30***and**

*35***, respectively. Find the area of triangle**

*84***.**

*ABC***TIPS:** Read more…

## 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.

**ANSWERS ARE** Read more…

## Triangle problem

Let triangle ABC be acute and let H be its orthocenter. The altitudes . Prove that

It is easy question. Use areas to solve it.

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## Quadrilateral & Circle problem

Quadrilateral ABCD is inscribed in a circle. Let AB = a, BC = b, CD = c, DA = d, AC = p and BD = q. Prove Ptolemy’s second theorem that .

This question is also taken from Bertley Math Circle .

It is easy question, just use a, b, c are sides of triangle and S is area of triangle.

If you couldn’t prove send me mail, and i will give few tips.

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