https://www.khanacademy.org/math/revision-tg-math-class-9/x6c9499d6e7016acd:week-3/x6c9499d6e7016acd:circles/v/basic-terms-related-to-circles 2026-02-22T07:10:45.705716181Z Basic Terms related to Circles What do dosas, rotis, and pizzas have in common? They're all circles! 🍕 This video uses delicious examples to introduce you to the fundamental parts of a circle. We'll explore the center, radius, diameter, chords, arcs, and sectors in a simple and visual way. Perfect for anyone starting their journey into geometry! Khan Academy video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Basic Terms related to Circles What do dosas, rotis, and pizzas have in common? They're all circles! 🍕 This video uses delicious examples to introduce you to the fundamental parts of a circle. We'll explore the center, radius, diameter, chords, arcs, and sectors in a simple and visual way. Perfect for anyone starting their journey into geometry! https://cdn.kastatic.org/ka-youtube-converted/BALZW-dY-fc.mp4/BALZW-dY-fc.mp4 350 Circles 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 Circles 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 Circles 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 Circles https://www.khanacademy.org/math/geometry/hs-geo-circles/hs-geo-circum-in-circles/v/constructing-circumscribing-circle 2021-02-16T16:08:13Z Geometric constructions: triangle-circumscribing circle Sal constructs a circle that circumscribes a given triangle using compass and straightedge. Sal Khan video https://cdn.kastatic.org/googleusercontent/V0uKUGvEasjML5uvY7GatUOHQWwIAk2a4xLm96HvKFrvB1pMwAyWu-hABihWDpXvR_BidO3JiJTaXKHzQNIUC_Qj Geometric constructions: triangle-circumscribing circle Sal constructs a circle that circumscribes a given triangle using compass and straightedge. https://cdn.kastatic.org/ka-youtube-converted/eSjbEWb4Qp4.mp4/eSjbEWb4Qp4.mp4 142 Circles https://www.khanacademy.org/math/class-9-tg/x06d55bfa213a79fd:circles/x06d55bfa213a79fd:angle-subtened-by-an-arc-of-a-circle/v/inscribed-angle-theorem-proof-indian-accent 2025-06-04T10:04:13.13703146Z Inscribed angle theorem proof Proving that an inscribed angle is half of a central angle that subtends the same arc. Kalakrit (Dubbing) video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Inscribed angle theorem proof Proving that an inscribed angle is half of a central angle that subtends the same arc. https://cdn.kastatic.org/ka-youtube-converted/2p1GEuOiUfA.mp4/2p1GEuOiUfA.mp4 856 Circles https://www.khanacademy.org/math/class-9-tg/x06d55bfa213a79fd:circles/x06d55bfa213a79fd:angles-in-the-same-segment/v/angles-subtended-by-an-arc-in-the-same-segment-are-equal 2026-02-11T08:39:31.456454846Z Angles subtended by an arc in the same segment are equal In this video, we explain the important circle theorem: angles subtended by an arc in the same segment are equal. The logic comes from the fact that each angle is subtended by the same arc, and the arc’s corresponding central angle governs their measure. By joining the arc’s endpoints to different points on the circle, we form triangles where the angles at the circumference depend on half the central angle. Since the central angle is fixed, all such angles in the same segment are equal. Step by step, we show the construction, the reasoning, and why this property holds true, making the theorem clear and easy to remember. Khan Academy video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Angles subtended by an arc in the same segment are equal In this video, we explain the important circle theorem: angles subtended by an arc in the same segment are equal. The logic comes from the fact that each angle is subtended by the same arc, and the arc’s corresponding central angle governs their measure. By joining the arc’s endpoints to different points on the circle, we form triangles where the angles at the circumference depend on half the central angle. Since the central angle is fixed, all such angles in the same segment are equal. Step by step, we show the construction, the reasoning, and why this property holds true, making the theorem clear and easy to remember. 126 Circles https://www.khanacademy.org/math/revision-term-1-mh-math-class-10/x041ca11815640a3a:week-3/x041ca11815640a3a:circle/v/inscribed-quadrilaterals-proof-indian-accent 2025-06-04T10:09:34.285343432Z Inscribed quadrilaterals proof Sal uses the inscribed angle theorem and some algebra to prove that opposite angles of an inscribed quadrilateral are supplementary. Kalakrit (Dubbing) video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Inscribed quadrilaterals proof Sal uses the inscribed angle theorem and some algebra to prove that opposite angles of an inscribed quadrilateral are supplementary. https://cdn.kastatic.org/ka-youtube-converted/Z6FqTdxIHJw.mp4/Z6FqTdxIHJw.mp4 236 Circles https://www.khanacademy.org/math/class-9-tg/x06d55bfa213a79fd:circles/x06d55bfa213a79fd:concyclic-quadrilateral/v/solving-inscribed-quadrilaterals-indian-accent 2025-06-04T10:09:34.285343432Z Solving inscribed quadrilaterals Example showing supplementary opposite angles in inscribed quadrilateral. Kalakrit (Dubbing) video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Solving inscribed quadrilaterals Example showing supplementary opposite angles in inscribed quadrilateral. https://cdn.kastatic.org/ka-youtube-converted/CGwvo1zLKAM.mp4/CGwvo1zLKAM.mp4 298 Circles https://www.khanacademy.org/math/revision-tg-math-class-9/x6c9499d6e7016acd:week-3/x6c9499d6e7016acd:circles/e/revision-circles-tg-class-9 2026-02-18T21:20:35.275198076Z Revision circles TG class 9 . Khan Academy exercise