Circle Geometry

Question 1

Answer 1

A triangle drawn from the two ends of a diameter will always make an angle of 90 where it hits the edge of the circle.

Question 2

Answer 2

A tangent always makes an angle of exactly 90 with the radius it meets at this point.

Question 3

Answer 3

They are isosceles because they are both radii.

Question 4

Answer 4

A chord is any line drawn across a circle, the line that cuts it exactly at in half (at 90) will go through the centre of the circle and so be the diameter.

Question 5

Answer 5

Angles in the same segment are equal, all triangles drawn from a chord will have the same angle where they touch the circle. Also the 2 angles on opposite sides of the chord will add up to 180.

Question 6

Answer 6

The angle suspended from the centre of a circle is exactly double the angle suspended at the edge of the circle from the same 2 points.

Question 7

Answer 7

Both pairs of opposite angles add up to 180 in a cyclic quadrilateral.

Question 8

Answer 8

The two tangents drawn from an outside point are always equal in length, so creating an isosceles situation with tow congruent right angled triangles.

Question 9

Answer 9

If a tangent and chord meet then the angle between them is always equal to the angle in the opposite segment