Αποτελέσματα Αναζήτησης
Created Date: 10/12/2015 2:00:50 PM
24 Ιαν 2022 · Descartes circle theorem Theorem (Descartes circle theorem, 1643) If b 1;b 2;b 3;b 4 are bends of four mutually tangent circles, then (b 1 + b 2 + b 3 + b 4) 2 = 2(b2 1 + b 2 2 + b 2 3 + b 2 4): Example 11 21 24 28 b 1 = 11, 2 = 21, 3 = 24, 4 = 28 ( 11 + 21 + 24 + 28)2 = 622 = 3844 2(( 11)2 + 212 + 242 + 282) = 2(1922) = 3844 Edna Jones The ...
28 Αυγ 2019 · Videos and Worksheets; Primary; 5-a-day. 5-a-day GCSE 9-1; 5-a-day Primary; 5-a-day Further Maths; More. Further Maths; GCSE Revision; Revision Cards; Books; Circle Theorem Proofs Practice Questions. Click here for Questions . Answers 1 Answers 2 Answers 3 Answers 4 Answers 5 Answers 6 . proof. Practice Questions. Previous: Area of a Segment ...
Descartes' circle theorem (a.k.a. the kissing circle theorem) provides a quadratic equation satisfied by the radii of four mutually tangent circles. By solving this equation, one can determine the possible values for the radius of a fourth circle tangent to three given, mutually tangent circles.
Revision for this topic. Prove that the angle in a semi-circle is always 90°. Prove that the angle at the centre is twice the angle at the circumference. Prove the angles in the same segment are equal. Prove the opposite angles in a cyclic quadrilateral add to 180°.
DESCARTES' CIRCLE THEOREM. If there exist three circles (C1, C2, C3, in black, below) that are mutually tangent externally and have radii r1, r2, r3, and a fourth circle (C4 in red, below - there are two possiblities) having radius r4 that is tangent to the first three, then the radii are related by ( 1 1 1 1. r.
In geometry, Descartes' theorem states that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain quadratic equation. By solving this equation, one can construct a fourth circle tangent to three given, mutually tangent circles.
