>, so a triangle made from two radii is [ ].","back":"All radii of the same circle are equal, so a triangle made from two radii is isosceles.","points":null},{"id":"bcc8b2a5-76ef-4725-8a35-e5491dd11f0a","cardType":"basic","front":"In triangle $AOB$ where $OA=OB$, what angle equality follows?","back":"$\\angle OAB=\\angle ABO$.","points":1},{"id":"d528e218-5a85-4512-8c33-fd0156c8465c","cardType":"cloze","front":"The angle at the centre is [ ] the angle at the circumference when both stand on the [ ].","back":"The angle at the centre is twice the angle at the circumference when both stand on the same arc.","points":null},{"id":"ef3183a4-9898-4549-97af-3fcb4a9c9b74","cardType":"basic","front":"In the centre-angle proof, if $\\angle PQO=x$, why is $\\angle OPQ=x$?","back":"$OP=OQ$, so triangle $OPQ$ is isosceles.","points":2},{"id":"29a85e08-b6e4-44f5-a938-d7cb5f872a0c","cardType":"basic","front":"In triangle $OPQ$, if the base angles are both $x$, what is $\\angle POQ$?","back":"$180^\\circ-2x$.","points":1},{"id":"06313807-c992-447e-810e-2d1587f8b3bc","cardType":"basic","front":"In the centre-angle proof, what central angle is obtained after subtracting $180^\\circ-2x$ and $180^\\circ-2y$ from $360^\\circ$?","back":"$2x+2y$.","points":1},{"id":"f38cf858-aae5-4020-938a-ab6b30369f0f","cardType":"basic","front":"If $\\angle PQO=x$ and $\\angle OQR=y$, what is $\\angle PQR$?","back":"$x+y$.","points":1},{"id":"398e7bdd-49c2-4e64-bae0-6a02c2f5378c","cardType":"cloze","front":"If a line passes through [ ] and both ends lie on the circle, it is a [ ].","back":"If a line passes through the centre and both ends lie on the circle, it is a diameter.","points":null},{"id":"0bebc2b9-4c13-4e2b-a6b6-9184b15dbeb3","cardType":"basic","front":"In the semicircle proof, why does $\\angle AOB+\\angle BOC=180^\\circ$?","back":"$AOC$ is a straight line.","points":2},{"id":"895d6063-5492-4514-ab8f-5164cde1613e","cardType":"basic","front":"What does $(180^\\circ-2x)+(180^\\circ-2y)=180^\\circ$ give for $x+y$?","back":"$x+y=90^\\circ$.","points":1},{"id":"2d60a4a2-9d77-4d0d-b677-4a146cc39e06","cardType":"cloze","front":"In a semicircle, the angle on the circumference opposite the diameter is [ ].","back":"In a semicircle, the angle on the circumference opposite the diameter is $90^\\circ$.","points":null},{"id":"4d22a0c0-6dc2-4819-9e36-6d61bf1103f7","cardType":"basic","front":"What can you conclude about two angles standing on the same chord on the same side of it?","back":"They are equal.","points":1},{"id":"fffef07e-cf99-4308-80b4-944daebb2c84","cardType":"basic","front":"Why are $\\angle ABD$ and $\\angle ACD$ equal when both stand on chord $AD$?","back":"Both are half of the same central angle, $\\angle AOD$.","points":2},{"id":"39e5c9b2-de70-4d96-ba48-b06168926564","cardType":"cloze","front":"A cyclic quadrilateral has all four vertices on the [ ] of a circle.","back":"A cyclic quadrilateral has all four vertices on the circumference of a circle.","points":null},{"id":"c055671d-285d-4698-84cd-5a010ba8282d","cardType":"basic","front":"In cyclic quadrilateral $ABCD$, what is $\\angle ABC+\\angle ADC$?","back":"$180^\\circ$.","points":1},{"id":"cd095f9f-0c36-4dca-890b-c5ffa2cc532a","cardType":"basic","front":"Why do opposite angles in a cyc

Proof of the Circle Theorems Flashcards

Proof of the Circle Theorems Flashcards

Proof of the Circle Theorems Flashcards

Proof of the Circle Theorems Flashcards