Circle properties：練習題

In a circle with centre \(O\), a line segment connects two points on the circumference and does not pass through the centre. What is the mathematical term for this line segment?

In a circle with centre \(O\), a chord \(AB\) has a length of \(16\text{ cm}\). The perpendicular distance from the centre \(O\) to the chord is \(6\text{ cm}\).
Calculate the radius of the circle.

In the diagram, points \(A\), \(B\), \(C\), and \(D\) lie on the circumference of a circle. Segment \(AC\) is a diameter of the circle. If the angle \(BDC = 38^\circ\), calculate the size of angle \(ACB\).

In a circle with centre \(O\), a line segment connects two points on the circumference. If this line segment passes through the centre \(O\), what is the specific name for this line?

In the diagram, points \(A\), \(B\), and \(C\) lie on the circumference of a circle with centre \(O\). If the angle \(AOC = 130^{\circ}\), calculate the size of the angle \(ABC\).

In the diagram, points \(P\), \(Q\), \(R\), and \(S\) lie on the circumference of a circle. If the angle \(PQR = 115^{\circ}\), calculate the size of the angle \(PSR\).

In the diagram, \(O\) is the centre of a circle. Points \(A\) and \(B\) lie on the circumference. \(ABC\) is a tangent to the circle at point \(B\). Given that \(OA\) is a radius and angle \(OAB = 35^{\circ}\):
(a) Find the size of the angle \(AOB\).
(b) Work out the size of the angle \(ABC\).
(c) State the geometric reason for the relationship between the radius \(OB\) and the tangent \(ABC\).