https://www.khanacademy.org/math/geometry/hs-geo-circles/xff63fac4:hs-geo-proofs-with-inscribed-shapes/v/right-triangles-inscribed-in-circles-proof 2022-10-07T00:00:24.225559754Z Proof: Right triangles inscribed in circles Proof showing that a triangle inscribed in a circle having a diameter as one side is a right triangle Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/15ef1dca-d313-4c4f-b62d-da49a3a29323_1280_720_base.png Proof: Right triangles inscribed in circles Proof showing that a triangle inscribed in a circle having a diameter as one side is a right triangle https://cdn.kastatic.org/ka-youtube-converted/b0U1NxbRU4w.mp4/b0U1NxbRU4w.mp4 335 Circle theorem I https://www.khanacademy.org/math/geometry/hs-geo-circles/hs-geo-tangents/v/proving-radius-is-perpendicular-to-tangent-line 2022-10-07T00:00:24.225559754Z Proof: Radius is perpendicular to tangent line Sal proves that the radius that connects the intersection point of a tangent line with the circle is perpendicular to the tangent line. video https://cdn.kastatic.org/ka_thumbnails_cache/34b0a898-d2a2-482b-8f82-1a9a124ef762_1280_720_base.png Proof: Radius is perpendicular to tangent line Sal proves that the radius that connects the intersection point of a tangent line with the circle is perpendicular to the tangent line. https://cdn.kastatic.org/ka-youtube-converted/St3MU5i3chc.mp4/St3MU5i3chc.mp4 521 Circle theorem I https://www.khanacademy.org/math/geometry/hs-geo-circles/hs-geo-tangents/a/determining-if-a-line-is-tangent-by-looking-at-angles 2024-01-22T04:05:23.075087325Z Determining tangent lines: angles Solve two problems that apply properties of tangents to determine if a line is tangent to a circle. article https://www.khanacademy.org/math/geometry/hs-geo-circles/hs-geo-tangents/a/determining-if-a-line-is-tangent-by-looking-at-lengths 2022-09-10T02:03:40.164764806Z Determining tangent lines: lengths Solve two problems that apply properties of tangents to determine if a line is tangent to a circle. article https://www.khanacademy.org/math/geometry/hs-geo-circles/hs-geo-inscribed-angles/v/inscribed-angles-exercise-example 2022-10-07T00:00:24.225559754Z Inscribed angles Sal finds a missing inscribed angle using the inscribed angle theorem.  video https://cdn.kastatic.org/ka_thumbnails_cache/88ed8757-3b40-4b35-afd1-f5085a99a2a0_1280_720_base.png Inscribed angles Sal finds a missing inscribed angle using the inscribed angle theorem.  https://cdn.kastatic.org/ka-youtube-converted/aNi1-zeEps8.mp4/aNi1-zeEps8.mp4 80 Circle theorem I https://www.khanacademy.org/math/geometry/hs-geo-circles/hs-geo-inscribed-angles/a/challenge-problems-inscribed-angles 2022-09-10T02:03:40.164764806Z Challenge problems: Inscribed angles Solve two challenging problems that apply the inscribed angle theorem to find an arc measure or an arc length. article https://www.khanacademy.org/math/geometry/hs-geo-circles/hs-geo-inscribed-angles/e/inscribed_angles_1 2026-03-18T02:40:44.778871182Z Inscribed angles Practice the relationship between inscribed & central angles that are subtended by the same arc length. Marcia Lee exercise https://www.khanacademy.org/math/cambridge-o-level-mathematics-4024/x3f4c73d082a798eb:geometry/x3f4c73d082a798eb:circle-theorem-i/v/proof-equal-chords-subtend-equal-angles-pk 2025-11-29T07:01:24.846724792Z Proof: Equal chords subtend equal angles Created by Khan Academy video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Proof: Equal chords subtend equal angles Created by Khan Academy https://cdn.kastatic.org/ka-youtube-converted/OnRdB1BVuKI.mp4/OnRdB1BVuKI.mp4 187 Circle theorem I https://www.khanacademy.org/math/cambridge-o-level-mathematics-4024/x3f4c73d082a798eb:geometry/x3f4c73d082a798eb:circle-theorem-i/e/chords-corresponding-to-congruent-arcs 2026-04-08T00:54:09.631945657Z Chords corresponding to congruent arcs In this exercise students learn about the congruent arcs and the theorems related to it, specially how the chords in congruent arcs behave and what can be deduced. Devashish Phadnis exercise https://www.khanacademy.org/math/geometry/hs-geo-circles/xff63fac4:hs-geo-proofs-with-inscribed-shapes/v/proving-the-opposite-angles-of-inscribed-quadrilateral-are-supplementary 2022-10-07T00:00:24.225559754Z Inscribed quadrilaterals proof Sal uses the inscribed angle theorem and some algebra to prove that opposite angles of an inscribed quadrilateral are supplementary. video https://cdn.kastatic.org/ka_thumbnails_cache/db83b754-b900-4a6e-9e59-841fd678f736_1280_720_base.png 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/LGnL17ESs3Q.mp4/LGnL17ESs3Q.mp4 236 Circle theorem I https://www.khanacademy.org/math/cambridge-o-level-mathematics-4024/x3f4c73d082a798eb:geometry/x3f4c73d082a798eb:circle-theorem-i/v/proof-angle-between-a-tangent-and-a-chord 2025-05-12T16:49:01.249479039Z Proof: Angle between a tangent and a chord Let's prove that the measure of the angle formed by the intersection of a tangent and a chord is half the measure of the intercepted arc. We'll construct an isosceles triangle and use the relationship between radii and tangents of a circle to convince ourselves that this is true for both the major and minor arcs formed. Sal Khan video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Proof: Angle between a tangent and a chord Let's prove that the measure of the angle formed by the intersection of a tangent and a chord is half the measure of the intercepted arc. We'll construct an isosceles triangle and use the relationship between radii and tangents of a circle to convince ourselves that this is true for both the major and minor arcs formed. https://cdn.kastatic.org/ka-youtube-converted/hbdvuygTlMA.mp4/hbdvuygTlMA.mp4 328 Circle theorem I