Class 10 ICSE Maths Circles Boards Questions
Here we provide Class 10 Maths important notes,board questions and predicted questions with Answers for chapter Circle. These important notes,board questions and predicted questions are based on ICSE board curriculum and correspond to the most recent Class 10 Maths syllabus. By practising these Class 10 materials, students will be able to quickly review all of the ideas covered in the chapter and prepare for the Class 10 Board examinations.
2016
Q1
In the figure given below AD is a diameter O is the centre of the circle AD is parallel to BC and
∠CBD = 32o Find:
(i) ∠ABD
(ii) ∠AOB
(iii) ∠BED
solutions
(i) ∠ABD
(ii) ∠AOB
(iii) ∠BED
solutions
Q2
In the given figure PQRS is a cyclic quadilateral PQ and SR produced meet at T
(i) Prove △TPS ~ △TRQ
(ii) Find SP if TP = 18cm, RQ = 4cm and TR = 6cm
solutions
(i) Prove △TPS ~ △TRQ
(ii) Find SP if TP = 18cm, RQ = 4cm and TR = 6cm
solutions
2017
Q3
In the given figure PQ is a tangent to the circle at A, AB and AD are bisectors of ∠CAQ and
∠PAC. If ∠BAQ = 30o, prove that:
(i) BD is a diameter of the circle
(ii) ABC is an isosceles triangle
solutions
(i) BD is a diameter of the circle
(ii) ABC is an isosceles triangle
solutions
Q4
In the figure given, O is the centre of the circle. ∠DAE = 70o, Find giving
suitable reasons the measure of:
(i) ∠BCD
(ii) ∠BOD
(iii) ∠OBD
solutions
(i) ∠BCD
(ii) ∠BOD
(iii) ∠OBD
solutions
2018
Q5
PQRS is a cyclic quadilateral. Given ∠QPS = 73o, ∠PSR = 82o,
calculate :
(i) ∠QRS
(ii) ∠RQS
(iii) ∠PRQ
solutions
(i) ∠QRS
(ii) ∠RQS
(iii) ∠PRQ
solutions
Q6
In the figure given below is the centre of the circle if QR = OP and ∠ORP = 20o.
Find the value of 'x' giving reasons
solutions
solutions
2019
Q7
In the given figure AC is a tangent to the circle with centre O
If ∠ADB = 55o, find x and y. Give reasons for your answers.
solutions
If ∠ADB = 55o, find x and y. Give reasons for your answers.
solutions
Q8
In the given figure ABCDE is a Pentagon inscribed in the circle such that AC is a diameter and side
BC || AE. If ∠BAC = 50o, find giving reasons :
(i) ∠ ACB
(ii) ∠ EDC
(iii) ∠BEC
Hence prove that BE is also a diameter.
solutions
(i) ∠ ACB
(ii) ∠ EDC
(iii) ∠BEC
Hence prove that BE is also a diameter.
solutions
2020
Q9
In the given figure, O is the center of the circle and AB is a diameter, if AC = BD and ∠AOC =
72o, Find :
(i) ∠ ABC
(ii) ∠ BAD
(iii) ∠ABD
solutions
(i) ∠ ABC
(ii) ∠ BAD
(iii) ∠ABD
solutions
Q10
In the given figure AB = 9cm, PA = 7.5cm and PC = 5cm
Chords AD and BC intersect at P
(i) Prove that △PAB ~ △PCD
(ii) Find the length of CD
solutions
Chords AD and BC intersect at P
(i) Prove that △PAB ~ △PCD
(ii) Find the length of CD
solutions
Q11
In the given figure TP and TQ are two tangents to the circle with center O, touching at A and C
respectively . If ∠BCQ = 55o and ∠BAP = 60o, find:
(i) ∠OBA and ∠OBC
(ii) ∠AOC
(iii) ∠ATC
solutions
(i) ∠OBA and ∠OBC
(ii) ∠AOC
(iii) ∠ATC
solutions
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