Common Segment Products for Circles
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- Let's say that we are given the above diagram, and we want to find the length of AEAEAE. Don't worry, we are told the lengths of BEBEBE, DEDEDE, and CECECE, so if we can find AE…
By Leigh Marie Braswell, Ryan Zhang, Moor Xu
- This post addresses the tangent/degenerate case of power of a point. Power of a Point states that, in the following diagram, PB‾×AP‾=PC‾×PD‾\overline{PB} \times \overline{AP}= \…
By Anthony Jiang, Victor Wang, Po-Shen Loh, Moor Xu
- When two chords intersect, as seen above, they are split in such a way where the product of the chord segments are equal. In Diagram DE(EB)=AE(EC)DE(EB) = AE(EC)DE(EB)=AE(EC)
By Matt P
- এখানে আমরা “Power of a point” নামে অত্যন্ত গুরুত্বপূর্ণ একটা থিওরেম নিয়ে আলোচনা করব। তো শুরু করা যাক। নিচের চিত্রটা দেখ। চিত্রে ABABAB এবং CDCDCD জ্যা দুটি পরস্পর PPP বিন্দুতে ছ…
By Tanmoy Kumar Sarkar, M Ahsan Al Mahir Lazim, Adib Hasan · বাংলা
Problems 5
- Suppose ΔABC\Delta ABCΔABC has AB=13,BC=14,CA=15AB = 13, BC = 14, CA = 15AB=13,BC=14,CA=15 with orthocenter HHH. The area of ΔBHC\Delta{BHC}ΔBHC can be expressed in the form ab\…
- The diameter of a circle is a line segment that stretches from 1 point on the circumference of a circle to the opposite side. However, a chord can be from any 2 points on a circ…
- Altitudes AP‾\overline{AP}AP and BQ‾\overline{BQ}BQ of an acute triangle △ABC\triangle ABC△ABC intersect at point HHH. If HP=5HP=5HP=5 while HQ=2HQ=2HQ=2, then calculate (BP)(P…
- সূক্ষ্মকোণী ত্রিভুজ △ABC\triangle ABC△ABC এর উচ্চতা APAPAP এবং BQBQBQ, HHH বিন্দুতে ছেদ করে। যদি HP=5HP=5HP=5 এবং HQ=2HQ=2HQ=2 হয়, তবে BP×PC−AQ×QCBP\times PC−AQ\times QCBP×PC−AQ…
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- PPP and QQQ are 2 points on the same circle centered at OOO. Another circle with POPOPO as diameter is drawn intersecting the chord PQPQPQ at AAA. If the radius of the larger ci…