K-12 Math Problems

Circle inscribed in a quadrant of another circle

lines — Tue, 03 Oct 2017 13:49:00 +0000

Circle inscribed in a quadrant of another circle

PROBLEM: A circle is inscribed in a quadrant of a circle whose radius is 10cm. Find the radius of the inscribed circle. Share your solution in the comment section.

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How to Prove the Central Angle – Inscribed Angle Theorem

lines — Sat, 23 Sep 2017 04:23:34 +0000

How to Prove the Central Angle – Inscribed Angle Theorem

When two secants intersect on the circle, it forms an inscribed angle. There are three cases in which the secants may be positioned as shown in the figure below. These positions form different cases for the central angle-inscribed angle relationship. So when you prove the theorem that the measure of the inscribed angle is half […]

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Four equal triangles problem

lines — Fri, 04 Aug 2017 03:06:00 +0000

Four equal triangles problem

Challenge yourself with this triangle problem. Squares were constructed on each side of triangle ABC. The free points of the squares were connected forming three more triangles. It is claimed that all the four triangles have equal area. Do they? Show that they do or don’t. Hints: Make a simpler problem. Use an isosceles triangle […]

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Squares, Triangles, and Van-Aubel’s Theorem

lines — Sat, 07 Jun 2014 11:27:04 +0000

Squares, Triangles, and Van-Aubel’s Theorem

Problem In the figure, H is the midpoint of side BC of ?ABC. The points I and J are the intersection of the diagonals of square ABDE and square ACGF respectively, that is they are the centers of the square. Prove that IH and HJ are congruent and that angle IHJ is a right angle. […]

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What is the point of tangency – no calculus, please

lines — Sun, 25 May 2014 12:32:24 +0000

What is the point of tangency – no calculus, please

Problem Two lines intersect the graph . The secant line intersects the graph at point A and B and the tangent line which is parallel to the secant, touches the graph at point E. You can read the coordinates of A and B from the graph but not E. What are the coordinates of E? […]

Original by lines