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WorksheetsAngle Properties of Circles
Total questions: 40
Worksheet time: 34mins
O is the centre and PT is a tangent to the circle at T.
Find the value of x.
(a)
O is the centre and PT is a tangent to the circle at T.
Find the values of x and y.
x = 45⁰, y = 90⁰
x = 45⁰, y = 45⁰
x = 90⁰, y = 45⁰
x = 90⁰, y = 90⁰
O is the centre and PT is a tangent to the circle at T.
Find the value of b.
(a)
O is the centre and PT is a tangent to the circle at T.
Find the values of a and b.
a = 35⁰, b = 110⁰
a = 55⁰, b = 70⁰
a = 72.5⁰, b = 35⁰
a = 35⁰, b = 55⁰
O is the centre and PT is a tangent to the circle at T.
Find the values of p, q and r.
p = 25⁰, q = 65⁰ and r = 25⁰
p = 25⁰, q = 32.5⁰ and r = 57.5⁰
p = 25⁰, q = 57.5⁰ and r = 32.5⁰
p = 25⁰, q = 57.5⁰ and r = 32.5⁰
O is the centre and PT is a tangent to the circle at T.
AOT and BOP are straight lines.
Find the values of a and b.
a = 85⁰, b = 80⁰
a = 80⁰, b = 80⁰
a = 85⁰, b = 85⁰
a = 80⁰, b = 85⁰
O is the centre, PA is a tangent to the circle at A.
AOC and PBC are straight lines.
Find the values of x, y and z.
x = 60⁰, y = 30⁰
and z = 90⁰
x = 30⁰, y = 60⁰
and z = 90⁰
x = 60⁰, y = 60⁰
and z = 90⁰
x = 90⁰, y = 30⁰
and z = 60⁰
O is the centre, PA is a tangent to the circle at A.
EOC and DOA are straight lines.
Find the values of x, y and z.
x = 100⁰, y = 40⁰
and z = 50⁰
x = 140⁰, y = 20⁰
and z = 70⁰
x = 120⁰, y = 30⁰
and z = 60⁰
x = 150⁰, y = 15⁰
and z = 75⁰
O is the centre, PA and QA are tangents to the circle at P and Q respectively.
Find the values of a, b and c.
a = 75⁰, b = 75⁰
and c = 60⁰
a = 80⁰, b = 80⁰
and c = 50⁰
a = 45⁰, b = 45⁰
and c = 30⁰
a = 90⁰, b = 90⁰
and c = 30⁰
O is the centre, PA and QA are tangents to the circle at P and Q respectively.
Find the values of a, b and c.
a = 11.5⁰, b = 75⁰
and c = 37.5⁰
a = 23⁰, b = 90⁰
and c = 67⁰
a = 23⁰, b = 90⁰
and c = 23⁰
a = 11.5⁰, b = 60⁰
and c = 30⁰
O is the centre of the circle.
PS and PT are tangents to the circle at S and T respectively.
Find the value of b.
(a)
O is the centre of the circle.
PS and PT are tangents to the circle at S and T respectively.
Find the value of c.
(a)
O is the centre of the circle.
PS and PT are tangents to the circle at S and T respectively.
Find the perimeter of quadrilateral OTPS.
(a)
O is the centre of the circle.
PS and PT are tangents to the circle at S and T respectively.
Find the area of quadrilateral OTPS.
(a)
O is the centre of the circle.
PA and PB are tangents to the circle at A and B respectively.
Find the value of x.
(a)
O is the centre of the circle.
PA and PB are tangents to the circle at A and B respectively.
Find the value of x.
(a)
O is the centre of the circle.
PA and PB are tangents to the circle at A and B respectively.
AODC and PBC are straight lines.
Find the value of a, b and c.
a = 55⁰, b = 70⁰
and c = 90⁰
a = 55⁰, b = 70⁰
and c = 55⁰
a = 65⁰, b = 35⁰
and c = 90⁰
a = 35⁰, b = 35⁰
and c = 55⁰
Given that BD = DC, ∠ABD = 42⁰ and ∠DBC = 65⁰,
calculate
∠BDC
(a)
Given that BD = DC, ∠ABD = 42⁰ and ∠DBC = 65⁰,
calculate
∠BAC
(a)
Given that BD = DC, ∠ABD = 42⁰ and ∠DBC = 65⁰,
calculate
∠DAB
(a)
Given that BD = DC, ∠ABD = 42⁰ and ∠DBC = 65⁰,
calculate
∠DEC
(a)
Find the values of x and y.
x = 30⁰, y = 30⁰
x = 80⁰, y = 30⁰
x = 30⁰, y = 80⁰
x = 15⁰, y = 40⁰
Find the values of c and d.
c = 30⁰, d = 30⁰
c = 30⁰, d = 65⁰
c = 65⁰, d = 65⁰
c = 65⁰, d = 30⁰
Find ∠ACB
(a)
Find ∠ADB
(a)
Find ∠ACD
(a)
Find ∠BAE
(a)
Find ∠BDC
(a)
Find the values of x and y.
x = 30⁰, y = 36⁰
x = 36⁰, y = 36⁰
x = 24⁰, y = 24⁰
x = 36⁰, y = 24⁰
Find the value of x
(a)
Find the value of y.
(a)
Find the value of a.
(a)
Given that O is the centre of the circle and
∠OBC = 20⁰,
calculate ∠BAC.
(a)
Find ∠ACB
(a)
In the diagram, O is the centre of the circle, and SP is parallel to RQ.
Calculate ∠PSR
(a)
In the diagram, O is the centre of the circle, and SP is parallel to RQ.
Calculate ∠OPQ
(a)
O is the centre of the circle and ABE is a triangle.
If the circle cuts BE at C and AE at D,
calculate ∠x, ∠y and ∠z.
x = 25⁰, y = 140⁰
and z = 15⁰
x = 30⁰, y = 110⁰
and z = 40⁰
x = 40⁰, y = 110⁰
and z = 30⁰
x = 15⁰, y = 140⁰
and z = 25⁰
In the diagram, P, Q, R and S are points on the circle.
PS and QR are produced to meet at A.
If ∠QSR = 35⁰, ∠QPA = 70⁰ and ∠RSA = 75⁰,
calculate ∠PQR.
(a)
In the diagram, P, Q, R and S are points on the circle.
PS and QR are produced to meet at A.
If ∠QSR = 35⁰, ∠QPA = 70⁰ and ∠RSA = 75⁰,
calculate ∠PAQ.
(a)
Given that OP = OQ, find the value of a.
(a)
