Circle theorems

Inscribed angles, tangents, chords, and the angle in a semicircle.

An angle inscribed in a circle is half the central angle on the same arc; an angle in a semicircle is a right angle; a tangent meets the radius at 90°; equal chords are equidistant from the centre. Picture it: slide the inscribed angle's vertex around the arc and its size never changes. Think it: all of these are one fact, the central angle theorem, applied to different configurations.

ຕົວຢ່າງທີ່ໄດ້ເຮັດ · circle radius 5

Geometry · Circles

Circle radius 5

ຂັ້ນຕອນຕໍ່ຂັ້ນຕອນ

r = 5
Everything about a circle follows from its radius.
d = 2r = 10
Diameter.
C = 2\pi r = 10 \pi \approx 31.416
Circumference.
A = \pi r^2 = 25 \pi \approx 78.540
Area.

ເປີດເຜີຍຄຳຕອບ

C = 10 \pi,\quad A = 25 \pi

ປັດຈຸບັນທ່ານ ເລືອກບັນຫາ ຫຼື ພິມ ຫຼື ແຕ້ມເອງ. ທຸກບາດກ້າວ, ຮູບ, ຄໍາຕອບຖືກລົບຈົນກວ່າເຈົ້າຈະຖາມມັນ.

ຮັກສາການເຮັດວຽກຂອງທ່ານໄວ້

ບັນຊີຟຣີ ເພີ່ມຂໍ້ມູນໃສ່ບົດຮຽນທຸກບົດ, ບັນທຶກຂອງສິ່ງທີ່ທ່ານໄດ້ເຮັດແລ້ວ, ບັນຫາທີ່ທ່ານໄດ້ແກ້ໄຂໄວ້ໃນບ່ອນດຽວ ແລະ ຄູສອນທີ່ທ່ານສາມາດຖາມກ່ຽວກັບໜ້ານີ້. ຄະນິດສາດເອງແມ່ນເປີດໃຫ້ທຸກຄົນ, ບໍ່ວ່າຈະໄດ້ເຂົ້າສູ່ລະບົບ ຫຼື ບໍ່.

ລົງທະບຽນ ចូល

ຕົວສະແດງທີ່ໃຊ້ຢູ່ທີ່ນີ້

ກົດຕົວອັກສອນໃດໜຶ່ງເພື່ອເບິ່ງຄວາມໝາຍເຕັມ, ຮູບ ແລະ ຕົວອັກສອນແຕ່ລະຕົວໃນມັນໝາຍຄວາມວ່າແນວໃດ.

ວິທີການ: Circle theorems

Find the centre and draw radii to every point on the circle in the problem.
Look for isosceles triangles (two radii). Their base angles are equal.
Apply the inscribed-angle or tangent, radius theorem to relate the angles, then solve.

ຄໍາຖາມທີ່ຄົນຖາມ

Why does every triangle have angles adding to 180°?

Draw a line through one vertex parallel to the opposite side: the two alternate angles equal the other two angles of the triangle, and the three angles at the vertex lie on a straight line. That is Euclid's proof, and it is why the fact holds only on a flat plane.

When do I use the law of sines versus the law of cosines?

Cosines when you know three sides, or two sides and the angle between them. Sines when you know an angle and the side opposite it, plus one more piece.

What is the difference between area and perimeter?

Perimeter is the length of the boundary (one dimension, measured in metres); area is the amount of surface inside (two dimensions, square metres). Doubling every side doubles the perimeter but quadruples the area.

ເພີ່ມເຕີມໃນ Geometry

Triangles Pythagorean theorem Circles Polygons Solids Coordinate geometry Euclid's axioms and the structure of proof Congruent and similar triangles Transformations: translation, rotation, reflection, dilation Solid geometry: prisms, pyramids, spheres