WISKUNDE
GRAAD 11
NOG OEFENINGE
Loodlyne op koorde.
GRAAD 11
NOG OEFENINGE
Loodlyne op koorde.
MATHEMATICS
GRADE 11
MORE EXERCISES
Perpendicular lines to a chord.
GRADE 11
MORE EXERCISES
Perpendicular lines to a chord.
O is die middelpunt van die sirkel. OQ ⊥ PR.
1.1 As OP = 5 cm, PR = 8 cm, bereken OQ. [ 1.1 ]
1.2 As OP = 13 cm, OQ = 5 cm, vind PR. [ 1.2 ]
1.3 As OQ = 8 cm, PR = 15 cm, vind OP. [ 1.3 ]
O is the center of the circle. OQ ⊥ PR.
1.1 If OP = 5 cm, PR = 8 cm, calculate OQ. [ 1.1 ]
1.2 As OP = 13 cm, OQ = 5 cm, vind PR. [ 1.2 ]
1.3 As OQ = 8 cm, PR = 15 cm, vind OP. [ 1.3 ]
Vind, met redes, die waarde van x en y
in elke figuur :
2.1 OM ⊥ AB; AB = 8 cm; OA = 5 cm;
AM = x; OM = y [ 2.1 ]
2.2 ME ⊥ CD; ME = 5 mm; MC = 13 mm;
CE = x; CD = y [ 2.2 ]
2.3 OM ⊥ AB; ON ⊥ CD; AB = 18 cm;
AB || CD; OC = 15 cm; CD = 24 cm ;
OM = x ; MON = y [ 2.3 ]
in elke figuur :
2.1 OM ⊥ AB; AB = 8 cm; OA = 5 cm;
AM = x; OM = y [ 2.1 ]
2.2 ME ⊥ CD; ME = 5 mm; MC = 13 mm;
CE = x; CD = y [ 2.2 ]
2.3 OM ⊥ AB; ON ⊥ CD; AB = 18 cm;
AB || CD; OC = 15 cm; CD = 24 cm ;
OM = x ; MON = y [ 2.3 ]
Find, giving reasons, the value of x and y
in each diagram :
in each diagram :
In die diagram is O die middelpunt van die sirkel
AO = 12 cm; AB = 14 cm; ON = √44
MO ⊥ AB;OP ⊥ AC; ON ⊥ BC
In the diagram O is the center of the circle
AO = 12 cm; AB = 14 cm; ON = √44
MO ⊥ AB;OP ⊥ AC; ON ⊥ BC
3.1 Bereken OM // Calculate OM [ 3.1 ]
3.2 Bereken BC // Calculate BC [ 3.2 ]
3.3 As AP = 4 cm en OP = √128 cm,
bewys dat OP ⊥ AC
If AP = 4 cm and OP = √128 cm,
prove that OP ⊥ AC [ 3.3 ]
AO = 12 cm; AB = 14 cm; ON = √44
MO ⊥ AB;OP ⊥ AC; ON ⊥ BC
In the diagram O is the center of the circle
AO = 12 cm; AB = 14 cm; ON = √44
MO ⊥ AB;OP ⊥ AC; ON ⊥ BC
3.1 Bereken OM // Calculate OM [ 3.1 ]
3.2 Bereken BC // Calculate BC [ 3.2 ]
3.3 As AP = 4 cm en OP = √128 cm,
bewys dat OP ⊥ AC
If AP = 4 cm and OP = √128 cm,
prove that OP ⊥ AC [ 3.3 ]
In die diagram is O die middelpunt van die sirkel
OR = 5 mm; OS = 7 mm; MN = 48 mm
OR ⊥ PQ; OS ⊥ MN.
Bepaal die lengte van PQ.
In the diagram O is the center of the circle
RO = 5 mm; OS = 7 mm; MN = 48 mm
OR ⊥ PQ; OS ⊥ MN.
Determine the length of PQ.
[ 4 ]
OR = 5 mm; OS = 7 mm; MN = 48 mm
OR ⊥ PQ; OS ⊥ MN.
Bepaal die lengte van PQ.
In the diagram O is the center of the circle
RO = 5 mm; OS = 7 mm; MN = 48 mm
OR ⊥ PQ; OS ⊥ MN.
Determine the length of PQ.
[ 4 ]
In die diagram is M die middelpunt van die sirkel
AC = 15 mm; AB = 15 mm; BC = 18 mm
AMD is 'n reguit lyn en AMD ⊥ BC.
Bepaal die lengte van AM.
In the diagram M is the center of the circle
AC = 15 mm; AB = 15 mm; BC = 18 mm
AMD is a straight line and AMD ⊥ BC.
Determine the length of AM.
[ 5 ]
AC = 15 mm; AB = 15 mm; BC = 18 mm
AMD is 'n reguit lyn en AMD ⊥ BC.
Bepaal die lengte van AM.
In the diagram M is the center of the circle
AC = 15 mm; AB = 15 mm; BC = 18 mm
AMD is a straight line and AMD ⊥ BC.
Determine the length of AM.
[ 5 ]
In die diagram is O die middelpunt van
die twee sirkels. Koord AD van die groot sirkel
sny die klein sirkel in B en C.
OB = 5 cm; BC = 6 cm; OD = 8,75 cm
Bepaal die lengte van AD en AB.
In the diagram O is the center of the two circles.
Chord AD of the bigger circle intersects
the smaller circle in B and C.
OB = 5 cm; BC = 6 cm; OD = 8,75 cm
Determine the length of AD and AB.
[ 6 ]
die twee sirkels. Koord AD van die groot sirkel
sny die klein sirkel in B en C.
OB = 5 cm; BC = 6 cm; OD = 8,75 cm
Bepaal die lengte van AD en AB.
In the diagram O is the center of the two circles.
Chord AD of the bigger circle intersects
the smaller circle in B and C.
OB = 5 cm; BC = 6 cm; OD = 8,75 cm
Determine the length of AD and AB.
[ 6 ]
