https://www.khanacademy.org/math/revision-term-1-od-math-class-10/x03e14a980a7a91ad:week-3/x03e14a980a7a91ad:circle/v/proof-equal-chords-subtend-equal-angles 2024-06-20T19:30:06.526648211Z Proof: Equal chords subtend equal angles In this video, we discuss the formal proof of the theorem which says that the equal chords that is the chords with same length subtend equal chord at the center of the circle. Devashish Phadnis video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Proof: Equal chords subtend equal angles In this video, we discuss the formal proof of the theorem which says that the equal chords that is the chords with same length subtend equal chord at the center of the circle. https://cdn.kastatic.org/ka-youtube-converted/vXFsXzXF-g4.mp4/vXFsXzXF-g4.mp4 207 Properties related to chord https://www.khanacademy.org/math/class-9-tg/x06d55bfa213a79fd:circles/x06d55bfa213a79fd:angle-subtended-by-a-chord-at-a-point/v/proof-when-two-chords-subtend-equal-angles-at-the-centre-the-chords-are-equal 2024-12-27T07:05:03.34880583Z Proof: When two chords subtend equal angles at the centre, the chords are equal Theorem: When two chords subtend an equal angle at the center the chords are equal in length. In this video we prove this statement using SAS test of congruency, and we use Manim to show beautiful animation. Devashish Phadnis video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Proof: When two chords subtend equal angles at the centre, the chords are equal Theorem: When two chords subtend an equal angle at the center the chords are equal in length. In this video we prove this statement using SAS test of congruency, and we use Manim to show beautiful animation. https://cdn.kastatic.org/ka-youtube-converted/OCNf1sBIwTs.mp4/OCNf1sBIwTs.mp4 187 Properties related to chord https://www.khanacademy.org/math/class-9-tg/x06d55bfa213a79fd:circles/x06d55bfa213a79fd:angle-subtended-by-a-chord-at-a-point/e/angles-inscribed-at-the-centre-by-a-chord 2026-04-07T22:23:57.656416987Z Angles inscribed at the centre by a chord this exercise is curated for new ncert and the problems are borrowed from 9.1 (circles) Devashish Phadnis exercise https://www.khanacademy.org/math/class-9-tg/x06d55bfa213a79fd:circles/x06d55bfa213a79fd:perpendicular-to-the-chord-and-equal-chords/v/proof-radius-is-perpendicular-to-a-chord-it-bisects-indian-accent 2025-06-04T10:04:13.13703146Z Proof: radius is perpendicular to a chord it bisects Lets prove that if a radius in a circle is drawn so it bisects a chord, then the radius is also perpendicular to that chord. The proof uses SSS congruence. Kalakrit (Dubbing) video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Proof: radius is perpendicular to a chord it bisects Lets prove that if a radius in a circle is drawn so it bisects a chord, then the radius is also perpendicular to that chord. The proof uses SSS congruence. https://cdn.kastatic.org/ka-youtube-converted/2nZ4kXK-46E.mp4/2nZ4kXK-46E.mp4 499 Properties related to chord https://www.khanacademy.org/math/class-9-tg/x06d55bfa213a79fd:circles/x06d55bfa213a79fd:perpendicular-to-the-chord-and-equal-chords/v/proof-perpendicular-radius-bisects-chord-indian-accent 2025-06-04T10:04:13.13703146Z Proof: perpendicular radius bisects chord Simple proof using right triangle-side-hypotenuse (RSH) congruence criterion to show that a radius perpendicular to a chord bisects it Kalakrit (Dubbing) video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Proof: perpendicular radius bisects chord Simple proof using right triangle-side-hypotenuse (RSH) congruence criterion to show that a radius perpendicular to a chord bisects it https://cdn.kastatic.org/ka-youtube-converted/Js9u5i8_HmQ.mp4/Js9u5i8_HmQ.mp4 233 Properties related to chord https://www.khanacademy.org/math/revision-term-1-mh-math-class-10/x041ca11815640a3a:week-3/x041ca11815640a3a:circle/v/proof-equal-chords-are-equidistant-from-the-center 2024-06-20T19:30:06.526648211Z Proof: Equal chords are equidistant from the center We discuss the proof of theorem which says that the equal chords of the circle are equidistant from the center. Devashish Phadnis video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Proof: Equal chords are equidistant from the center We discuss the proof of theorem which says that the equal chords of the circle are equidistant from the center. https://cdn.kastatic.org/ka-youtube-converted/NglXukgt-GM.mp4/NglXukgt-GM.mp4 312 Properties related to chord https://www.khanacademy.org/math/class-9-tg/x06d55bfa213a79fd:circles/x06d55bfa213a79fd:perpendicular-to-the-chord-and-equal-chords/v/chords-equidistant-from-the-centre-of-the-circle-are-equal-in-length 2026-02-11T08:39:31.456454846Z Chords equidistant from the centre of the circle are equal in length This video explains why chords equidistant from the centre of a circle are equal in length, using the concept of congruency. By drawing perpendiculars from the centre to each chord, we form two right triangles. Since the perpendiculars are equal and the radii are equal, the triangles are congruent. From this congruency, it follows that the corresponding chord segments are equal, proving that the chords themselves are equal in length. Khan Academy video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Chords equidistant from the centre of the circle are equal in length This video explains why chords equidistant from the centre of a circle are equal in length, using the concept of congruency. By drawing perpendiculars from the centre to each chord, we form two right triangles. Since the perpendiculars are equal and the radii are equal, the triangles are congruent. From this congruency, it follows that the corresponding chord segments are equal, proving that the chords themselves are equal in length. 197 Properties related to chord https://www.khanacademy.org/math/class-9-tg/x06d55bfa213a79fd:circles/x06d55bfa213a79fd:perpendicular-to-the-chord-and-equal-chords/e/perpendicular-from-the-center-to-a-chord 2026-02-20T04:00:32.356270105Z Perpendicular from the center to a chord In this exercise, we will learn how to implement the following properties of chords of a circle. (1) The perpendicular from the centre of a circle to a chord bisects the chord. (2) The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord (3) Equal chords are equidistant from the centre Khan Academy exercise