# Math Is Fun Forum

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## #1 Re: Exercises » nine squares » 2023-06-01 07:02:16

very good phrontister

## #2 Exercises » nine squares » 2023-05-28 00:01:08

tony123
Replies: 2

Olivia cut a rectangle into exactly nine squares. On inspection, he observed that the area of one square was 64 cm²
, the areas of two other squares were 16 cm²
, and the rest of them were 4 cm²
each.
What was the perimeter of the original rectangl

## #3 Exercises » isosceles right-angled triangle » 2023-04-21 20:09:39

tony123
Replies: 1

The isosceles right-angled triangle ABC
has its right angle at C. D is an interior point of side BC such that the angle CDA
is 75°. Given that triangle ADC has unit area, prove that BD=2.

## #4 Exercises » convex hexagon » 2023-03-17 06:27:53

tony123
Replies: 9

The opposite sides of a convex hexagon

are parallel, the distances separating the parallel pairs of sides are equal,
and the angles at vertices A and D are right angles. Prove that the diagonals BE
and CF enclose an angle of

## #5 Re: Exercises » the largest possible » 2023-03-10 16:12:40

Thanks Bob great job

## #6 Exercises » the largest possible » 2023-03-02 18:19:43

tony123
Replies: 3

Find, without calculus, the largest possible value of

(sin 5x + cos 3x)/(sin 4x + cos 4x)

## #7 Exercises » interval » 2022-12-01 20:11:16

tony123
Replies: 1

if the two roots of the equation

are elements of the interval
find the interval of

## #8 Re: Exercises » In triangle ABC » 2022-02-12 10:27:39

hi bob
There is an important theorem in the external bisector of an angle in a triangle

## #9 Exercises » In triangle ABC » 2022-02-11 05:14:52

tony123
Replies: 3

In ∆ ABC, AB =7, AC=5.An external bisector of
∠BAC intersects the circumcircle of
∆ABC at E. Let F be the foot of
perpendicular from E to line AB.
find AF

## #10 Re: Exercises » Find the real solutions » 2022-01-19 21:18:25

Now we can say great job
Thanks bob

## #11 Re: Exercises » Find the real solutions » 2022-01-11 08:08:08

There are some mistakes in your solution dear Bob

nice work
thanks Bob

## #13 Exercises » Find the real solutions » 2022-01-10 07:36:40

tony123
Replies: 8

Find the real solutions of the  two equations

(1)

(2)

## #14 Exercises » congruent » 2022-01-09 21:30:07

tony123
Replies: 4

Prove that if two right-angled triangles

have the same perimeter and the same area,
then they are congruent.

## #15 Re: Exercises » solve equation » 2022-01-07 04:16:06

hi bob
I'm glad you liked these problems
For the acute angles problem,
Someone sent this solution hope you like it

tony123
Replies: 4

find x

## #17 Exercises » prove » 2021-12-03 01:31:16

tony123
Replies: 0

Let

and
be acute angles such that
. Prove that
.

## #18 Exercises » In an acute-angled » 2021-11-15 16:32:15

tony123
Replies: 1

In an acute-angled triangle ABC, a tangent is drawn to the inscribed circle, parallel to side BC. The tangent intersects side AC at point D. F is the orthogonal projection of point D onto the side BC. Show that AB=AD+BF

## #19 Exercises » solve » 2021-11-06 08:06:08

tony123
Replies: 1

1.solve in

|x+2|≥|x+1|
2.if
find the valuo of

tony123
Replies: 11

hard

tony123
Replies: 4

from Μιχάλης

## #22 Exercises » find area » 2020-04-29 23:32:58

tony123
Replies: 1

from Mr Παύλος

M,N,Z,I midpoint

find the area of  EMBN

tony123
Replies: 17

find AB

FROM Mr Doloros

## #24 Exercises » ordered pair » 2020-03-29 06:05:29

tony123
Replies: 1

What is the ordered pair of real numbers (x,y) for which
123x+ 321y= 345
and

321x+ 123y= 543?

hi bob
Just for fun