https://www.khanacademy.org/math/geometry-tx/x790e3ac3e338c450:relationships-of-circles-including-radian-measure-and-equations-of-circles/x790e3ac3e338c450:properties-of-secants/v/proof-the-product-of-segments-of-intersecting-secants 2025-05-12T16:49:01.249479039Z Proof: The product of segments of intersecting secants Let's prove that the product of the length of a secant segment and its external segment is equal to the product of the other secant segment and its external segment from the same point outside the circle. We'll construct similar triangles and use the properties of inscribed triangles to convince ourselves that this is always true. Sal Khan video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Proof: The product of segments of intersecting secants Let's prove that the product of the length of a secant segment and its external segment is equal to the product of the other secant segment and its external segment from the same point outside the circle. We'll construct similar triangles and use the properties of inscribed triangles to convince ourselves that this is always true. https://cdn.kastatic.org/ka-youtube-converted/J3FpOlIkH3Q.mp4/J3FpOlIkH3Q.mp4 190 Properties of secants https://www.khanacademy.org/math/geometry-tx/x790e3ac3e338c450:relationships-of-circles-including-radian-measure-and-equations-of-circles/x790e3ac3e338c450:properties-of-secants/v/proof-angle-formed-by-intersecting-secants 2025-05-12T16:49:01.249479039Z Proof: Angle formed by intersecting secants Let's prove that the measure of the angle formed by 2 secants intersecting at a point outside the circle is half the difference of the measures of the intercepted arcs. We'll construct a triangle and use the properties of inscribed angles to convince ourselves that this is always true. Sal Khan video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Proof: Angle formed by intersecting secants Let's prove that the measure of the angle formed by 2 secants intersecting at a point outside the circle is half the difference of the measures of the intercepted arcs. We'll construct a triangle and use the properties of inscribed angles to convince ourselves that this is always true. https://cdn.kastatic.org/ka-youtube-converted/dHP6PxXlrV0.mp4/dHP6PxXlrV0.mp4 272 Properties of secants https://www.khanacademy.org/math/geometry-tx/x790e3ac3e338c450:relationships-of-circles-including-radian-measure-and-equations-of-circles/x790e3ac3e338c450:properties-of-secants/v/proof-the-product-of-segments-of-intersecting-secant-and-tangent 2025-05-12T16:49:01.249479039Z Proof: The product of segments of intersecting secant and tangent Let's prove that the product of the length of a secant segment and its external segment is equal to the square of the length of the tangent segment intersecting the secant segment at a point outside the circle. We'll construct a pair of similar triangles and use the properties of inscribed angles, tangents, and chords to convince ourselves that this is always true. Sal Khan video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Proof: The product of segments of intersecting secant and tangent Let's prove that the product of the length of a secant segment and its external segment is equal to the square of the length of the tangent segment intersecting the secant segment at a point outside the circle. We'll construct a pair of similar triangles and use the properties of inscribed angles, tangents, and chords to convince ourselves that this is always true. https://cdn.kastatic.org/ka-youtube-converted/BnpRSGP4TTE.mp4/BnpRSGP4TTE.mp4 246 Properties of secants https://www.khanacademy.org/math/geometry-tx/x790e3ac3e338c450:relationships-of-circles-including-radian-measure-and-equations-of-circles/x790e3ac3e338c450:properties-of-secants/v/proof-angle-between-a-tangent-and-a-secant 2025-05-12T16:49:01.249479039Z Proof: Angle between a tangent and a secant Prove that the measure of the angle formed by a secant and a tangent intersecting at a point outside the circle is half the difference of the measures of the intercepted arcs. We'll construct a triangle, then use the properties of inscribed angles, tangents, and chords to convince ourselves that this is always true. Sal Khan video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Proof: Angle between a tangent and a secant Prove that the measure of the angle formed by a secant and a tangent intersecting at a point outside the circle is half the difference of the measures of the intercepted arcs. We'll construct a triangle, then use the properties of inscribed angles, tangents, and chords to convince ourselves that this is always true. https://cdn.kastatic.org/ka-youtube-converted/OzeHAwjaG60.mp4/OzeHAwjaG60.mp4 208 Properties of secants https://www.khanacademy.org/math/geometry-tx/x790e3ac3e338c450:relationships-of-circles-including-radian-measure-and-equations-of-circles/x790e3ac3e338c450:properties-of-secants/e/secants-in-circles 2025-06-18T00:19:07.478052439Z Secants in circles Given a point outside of a circle and 2 secant lines or a secant line and a tangent line from the point that intersect the circle, along with some relevant measures, calculate the missing measurements. Charlie Auen exercise