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benjamingu22

20 Questions
5 Answers

0

1515

7

+99

Circles and Angles

Let be a cyclic quadrilateral. Let be the intersection of and , and let be the intersection of and . Prove that the angle bisectors of and are perpendicular. read more ..

Melody ●●●●●●●

benjamingu22 Nov 12, 2017

+1

1251

1

+99

Funky Circle Areas

Let be the union of the set of all points inside a regular nonagon with side length units and the set of all points less than unit away from a point on the perimeter of the nonagon. What, in units, is the perimeter of ? read more ..

benjamingu22 Nov 10, 2017

0

1096

1

+99

Special Parts of a Triangle, Continued!

Medians and of are perpendicular at point . Prove that .

In your diagram, should appear to be a right angle.

benjamingu22 Sep 30, 2017

0

1129

2

+99

Special Parts of a Triangle

A circle is drawn that intersects all three sides of as shown below. Prove that if , then the center of the circle is the incenter of .

read more ..

benjamingu22 Sep 24, 2017

0

941

1

+99

More Right Triangles!

Quadrilateral has right angles at and and an acute angle at . Altitudes are dropped from and to diagonal , meeting at and as shown. Prove that .
read more ..

benjamingu22 Sep 14, 2017

0

902

1

+99

Similar Triangles and Right Triangles

Point is inside rectangle . Show that

Be sure that your proof works for ANY point inside the rectangle.

benjamingu22 Sep 10, 2017

+3

2234

3

+99

MATHCOUNTS State

The region shown is bounded by the arcs of circles having radius 4 units, having a central angle measure of 60 degrees and intersecting at points of tangency. The area of the region can be expressed in the form square units, where is read more ..

hectictar ●●●

benjamingu22 Sep 5, 2017

0

983

1

+99

Similar Triangles

Triangle has a right angle at . Legs and are extended past point to points and , respectively, such that . Prove that .

benjamingu22 Aug 30, 2017

0

1162

3

+99

Isosceles & Equilateral Triangles, Perimeter, and Area

Let be any triangle. Equilateral triangles , , and are constructed such that none of these triangles overlaps triangle .

(a) Draw a triangle and then sketch the remainder of the figure. read more ..

benjamingu22 Aug 23, 2017

+2

2499

1

+99

Isosceles & Equilateral Triangles, Perimeter, and Area

The diagram shows a rectangle that has been dissected into nine non-overlapping squares. Given that the width and the height of the rectangle are relatively prime positive integers (meaning two integers whose largest common divisor is 1), find the perimeter read more ..

benjamingu22 Aug 22, 2017

+99

+1

Thank you, CPhill.

benjamingu22Jun 8, 2017

+99

+1

Thank you, CPhill.

benjamingu22Jun 1, 2017

+99

+1

Thank you, Guest.

benjamingu22Jun 1, 2017

+99

+1

How did you get $r=-\frac{4}{5}$ ?

benjamingu22Jun 1, 2017

+99

+1

How did you get $r=-\frac{1}{2}$ ?

benjamingu22Jun 1, 2017