10/10/2023 0 Comments Equidistant chord geometry![]() ∴ Points B and C are equidistant from any point of line m ….(ii) ∴ Points A and B are equidistant from any point of line l ….(i)ĭraw the perpendicular bisector of seg BC (line m) to intersect line l at point P. Let points A, B, C be any three non collinear points.ĭraw the perpendicular bisector of seg AB (line l). Is it possible to draw one more circle passing through these three points? Think of it. What should be done to draw a circle passing through all these points? Draw a circle through these points. We can draw infinite number of circles passing through A and B.Īll their centres will lie on the perpendicular bisector of AB (i.e., line l) ∴ The circle with centre Q and radius QA passes through point B. The circle with any other point Q and radius QA is drawn. ∴ The circle with centre P and radius PA passes through point B. Line l is the perpendicular bisector of seg AB.Įvery point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment. Draw the circle with centre P and radius PA. How many such circles can be drawn, passing through A and B? Where will their centres lie? (Textbook pg. Taking any other point Q on the line l, if a circle is drawn with centre Q and radius QA, will it pass through B? Think. Observe that the circle passes through point B also. Draw perpendicular bisector l of the segment AB. Test of congruency useful in solving the above problem is AAS ISAAI test of congruency. The chords which are equidistant from the centre are equal in length. Using appropriate test and theorem write the proof of the above example. Which of the following tests of congruence of triangles will be useful?Ī. Congruent chords of a circle are equidistant from the centre. The chords which are equidistant from the centre are equal in length.ī. To solve this problem which theorems will you use?Ī. In the adjoining figure, M is the centre of the circle and seg AB is a diameter, seg MS ⊥ chord AD, seg MT ⊥ chord AC, ∠DAB ≅ ∠CAB. ∴ The distance of point C from line AB is 6 cm. line AB is the tangent to the circle with centre C and radius AC. What is the distance of point C from line AB? Why? In the adjoining figure, the radius of a circle with centre C is 6 cm, line AB is a tangent at A. "Chords equidistant from the center of circle are equal in Algebraden.Maharashtra State Board Class 10 Maths Solutions Chapter 3 Circle Practice Set 3.1 Hence, this proves property 6 of circle i.e. Put the values from above statement 2 & 3 and we get: Since, we know that corresponding parts of congruent triangles are equal, so we get: Therefore, on applying RHS Rules of congruency, we get: ![]() ![]() OQ = OR (radii of circle are always equal) Now, join points O & Q and O & R (as shown below):Īngle 1 = Angle 2 (90 degree each - proved in above statement 1) Similarly, O is the center of circle (given)Īnd OB is perpendicular to RS (proved in above statement 1) So apply Property 3 of circle, "The perpendicular from the center of a circle to a chord bisects the chord" and we get: (statement 1)Īnd OA is perpendicular to PQ (proved in above statement 1) OA is perpendicular to PQ and OB is perpendicular to RS (as shown below). Since OA and OB is the distance of chords PQ & RS respectively from the center of circle.Īnd as per the property which says "The length of perpendicular from a point to a line is the distance of line from the point", so we get: Property : Perpendicular from the center of a circle to a chord bisects the chord What are Corresponding Parts of Congruent Triangles ? What is RHS Rule of congruency in Triangles ? How to prove this property : Chords equidistant from the center of circle are equal in lengthīefore you prove this property, you are advised to read: Now, as per the property 6 of circle i.e."Chords equidistant from the center of circle are equal in length", we get: OA and OB is the distance of chords PQ & RS respectively from the center of circle What is Distance of a Line from the point ? Line drawn from the center of circle to bisect a chord, is perpendicular to the chordĮqual chords are equidistant from the center of circleĬhords equidistant from the center of circle are equal in lengthīefore you understand the property "Chords equidistant from the center of circle are equal in length", you are advised to read: Perpendicular from the center of a circle to a chord bisects the chord If Angles subtended by the chords at the center of circle are equal, then chords are also equal Home > Circle > Properties of Circle > Chords equidistant from the center of circle are equal in length > Chords equidistant from the center of circle are equal in lengthĮqual chords subtend equal angles at the center of a circle
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |