Circles Lines Intersection

The diagram shows a circle with centre O and a radius of 5 cm. The circle is divided into 8 equal parts.

Which two points are intersections of two loci which are always 5 cm from point O and 5 cm from the line LOQ?

• L and Q

• N and S

• M and R

• K and P

The diagram shows two circles with centres O and P. Given OP = 4 cm, S is the midpoint of OP and Q is the midpoint of SP. A point L moves such that it is always 3 cm from point O. A point M moves such that it is always 2 cm from point P. Which of the following points are the intersection of locus L and locus M?

• S and T

• Q and R

• R and T

• P and T

In the diagram, PQRS is a square. PTR is an arc of a circle with centre S. QUS is an arc of a circle with centre P. X is the locus of a point which moves such that its distance from S is always constant. Y is the locus of a point which moves such that it is equidistant from the lines PQ and QR. Which of the points, A, B, C or D, is the intersection of the locus X and the locus Y?

• A

• B

• C

• D

In the diagram, P is the common centre of two circles, KRUQM and LTN, while Q is the common centre of the circles KLPUS and MNT.

A point Y moves such that it is always equidistant from points R and S.

The locus of Y is

• the arc KM.

• the straight line KU.

• the arc LN.

• the straight line LM.

Which best describes line AB?

• chord

• secant

• tangent

• diameter

The point of intersection of the line and the circle is referred to as?

• center point

• point of tangency

• point of exclamation

• intercepted point

Line QR

• Chord

• Secant

• Diameter

• Radius

What best describes segment AB?

• chord

• secant

• tangent

• diameter

Which best describes line AB?

• chord

• secant

• tangent

• diameter

In the diagram, PQR is an equilateral triangle with sides of 4 cm. UM and KL are two circular arcs with Q as the centre. K is the midpoint of UP.
X is the locus of a point which moves such that its distance from Q is always 3 cm. Y is the locus of a point which moves such that YQ = YR. The point of intersection of the locus X and locus Y is

• N

• P

• M

• L