If O is the centre of the circle, find the value of x in each of the following figures
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Circles question types
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94
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01
[1 Mark Question Answer]
6 Q→02[2 Mark Question Answer]
26 Q→03[3 marks sum]
39 Q→04[4 marks sum]
23 Q→Sample Questions
Circles questions
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If O is the centre of the circle, find the value of x in each of the following figures
In the figure given below, $PT$ is a tangent to the circle. Find $PT$ if $AT = 16\ cm$ and $AB = 12\ cm$.
View full solution →In Fig., chords AB and CD of the circle intersect at O. AO = 5 cm, BO = 3 cm and CO = 2.5 cm. Determine the length of DO.
In Fig. AT is a tangent to the circle. If m∠ABC = 50°, AC = BC, Find ∠BAT.
AB is a diameter of a circle with centre C = (- 2, 5). If A = (3, – 7). Find
(i) the length of radius AC
(ii) the coordinates of B.
(i) the length of radius AC
(ii) the coordinates of B.
C is a point on the minor arc AB of the circle, with centre O. Given ∠ACB = x° and ∠AOB = y° express y in terms of x. Calculate x, if ACBO is a parallelogram.
Find the length of a chord which is at a distance of $5 \ cm$ from the centre of a circle of radius $13 \ cm.$
View full solution →In the adjoining figure, AB is the diameter of the circle with centre O. If ∠BCD = 120°, calculate:
(i) ∠BAD (ii) ∠DBA
(i) ∠BAD (ii) ∠DBA
In the figure, ∠ DBC = 58°, BD is diameter of the circle.
Calculate:
(i) ∠ BDC
(ii) ∠ BEC
(iii) ∠ BAC
Calculate:
(i) ∠ BDC
(ii) ∠ BEC
(iii) ∠ BAC
The radius of a circle is $13 \ cm$ and the length of one of its chord is $10 \ cm$. Find the distance of the chord from the centre.
View full solution →In the given figure, diameter $AB$ and chord $CD$ of a circle meet at P . $PT$ is a tangent to the circle at T . $CD =7.8 cm, PD$ $=5 cm, PB =4 cm$. Find: (i) AB . (ii) Find the length of tangent $PT.$
View full solution →In the figure, AC is the diameter of circle, centre O. Chord BD is perpendicular to AC. Write down the angles p, q, r in term of x.
In the figure given alongside, AD is the diameter of the circle. If ∠ BCD = 130°, Calculate: (i) ∠ DAB (ii) ∠ ADB.
In the figure alongside PR is a diameter of the circle, PQ = 7 cm; QR = 6 cm and RS = 2 cm. Calculate the perimeter of the cyclic quadrilateral PQRS.
In the diagram given alongside, AC is the diameter of the circle, with centre O. CD and BE are parallel. ∠ AOB = 80° and ∠ ACE = 10°. Calculate: (i) ∠ BEC (ii) ∠ BCD (iii) ∠ CED.
In triangle PQR, PQ = 24 cm, QR = –7 cm and ∠PQR = 90°. Find the radius of the inscribed circle.
In the figure alongside O is the centre of circle ∠ XOY = 40°, ∠ TWX = 40° and XY is parallel to TZ.
Find: (i) ∠ XZY, (ii) ∠ YXZ (iii) ∠ TZY.
Find: (i) ∠ XZY, (ii) ∠ YXZ (iii) ∠ TZY.
In the adjoining figure, O is the centre of the circle and AB is a tangent to it at point B. ∠BDC = 65° Find ∠BAO.
In the figure, AB = AC = CD, ∠ADC = 38°. Calculate: (i) ∠ ABC, (ii) ∠ BEC.
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