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Circles 10 Old

The document is a practice paper for Class X students at St. Anthony's School focusing on the topic of circles. It contains various geometry problems related to angles, diameters, chords, and tangents, requiring students to calculate specific angles and lengths based on given figures. The exercises are designed to enhance students' understanding of circle properties and theorems.

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Maninder sng Kshatriya
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7 views5 pages

Circles 10 Old

The document is a practice paper for Class X students at St. Anthony's School focusing on the topic of circles. It contains various geometry problems related to angles, diameters, chords, and tangents, requiring students to calculate specific angles and lengths based on given figures. The exercises are designed to enhance students' understanding of circle properties and theorems.

Uploaded by

Maninder sng Kshatriya
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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CLASS X

CIRCLES
ST ANTHONY’S SCHOOL GIRLS’
SIR DEVEN’S PRACTICE PAPER

2. In the figure (a) given below, O is the centre of the circle. If angle AOB = 1400 and
angle OAC = 500, find:
(i) angle ACB(ii) angle OBC (iii) angle OAB (iv) angle CBA

3. In the figure (b) given below, AB is a diameter of the circle APBR. APQ and RBQ
are straight lines, angle A = 350, angle Q = 250. Find:
(i) angle PRB (ii) angle PBR (ii) angle BPR

a b

4.

Find: DEC Find: CDE and OBE

5.

Find: CED Find x

6.

Find: ABC, ADC Find: ABC, EAF

7.
Find: CAD, CBD, ADC Find: ABC and CB

8.

Find: p, q, r Find: RPQ and STP Find: CAB


9.

OBA = 450, ADE = 700 Find: PST


Find: OCA , BAC Find: x, y

10. a) In the figure (i) given below, DB is a diameter, calculate:


(i) QAB (ii) PAD (iii) CDB
b) In the figure (ii) given below, find angle CAB.

(i) (ii)
11. a) In the figure (i) given below, AB is a diameter, calculate angle ATB
b) In the figure (ii) given below, angle SPT = 840 find angles: TOS and TQS
(i) (ii)

12. In the adjoining figure, O is the centre of the circle.


If angle ACO = 550, find:
(i) BCO
(ii) AOB
(iii) APB

13. a) In the figure (i) given below, AB is parallel to CD and angle ABC = 550, find
(i) BOD (ii) BPD
b) In the figure (ii) given below, AB is a diameter, If angle BPT’ = 300, find:
(i) APT (ii) BOP

(i) (ii)

14. a) In the figure (i) given below, AB is a diameter. Angle CAB = 340. Find:
(i) CBA (ii) CQA
b) In the figure (ii) given below, angle APB = 600, find:
(i) AOB (ii) OAB (iii) ACB

15. Two chords AB, CD of a circle intersect internally at a point P. If:


(i) AP = 6cm, PB = 4cm and PD = 3cm, find PC
(ii) AB = 12cm, AP = 2cm and PC = 5cm, find PD
(iii) AP = 5cm, PB = 6cm and CD = 13cm, find CP

16. a) In the figure (i) given below, find TP if AT = 16cm and AB = 12cm.
b) In the figure (ii) given below, AB is a diameter. CD = 7.8cm, PD = 5cm,
PB = 4cm. Find:
(i) AB (ii) length of the tangent PT.
(i) (ii)
17. In the figure given below, CBA is a secant and CD is tangent to the circle. If
AB = 7cm and BC = 9 cm, then,
(i) Prove that Δ ACD Δ DCB
(ii) Find the length of CD

18. a) In the figure (i) given below, angle BAT = 450, BAC = 650, Find ABC.
b) In the figure (ii) given below, angle ATC = 360 and angle ACT = 480,
calculate the angle subtended by AB at the centre of the circle

19. Find the value of x in the following figures:

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