CBSE practice Questions

Extra Questions for Maths Circles

questions on circles for class 9

Extra Questions for Maths Circles with Answers:

Question: A circle touches the sides of a quadrilateral ABCD at P, Q, R, S respectively. Show that the angles subtended at the centre by a pair of opposite sides are supplementary.

Question: Two circles intersect at two points A and B. AD and AC are diameters to the two circles (in figure). Prove that B lies on the line segment DC.

Question: Prove equal chords of a circle subtend equal angles at the centre.

Question: A triangle ABC has incentre I and the incircle touches BC, CA at D,E respectively. If BI meets DE in G, show that AG is perpendicular to BG.

Related: General Science MCQ Question Answer

Question: ABC and ADC are two right triangles with common hypotenuse AC. Prove that ∠CAD = ∠CBD.

Question: Let P be an interior point of an equilateral triangle ABC such that  Prove that ∠BPC=1500

Question: Two circles intersect at two points B and C. Through B, two line segments ABD and PBQ are drawn to intersect the circles at A, D and P, Q respectively. Prove that ∠ACP = ∠ QCD.

circle-question-2

Question: If two circles intersect at two points, prove that their centres lie on the perpendicular bisector of the common chord.

Question: In the following figure, AB is a diameter of the circle with centre O, If AC and BD are perpendiculars on a line PQ, and BD meets the circle at E, prove that AC = ED.

Question: A

Question: If two intersecting chords of a circle make equal angles with the diameter passing through their point of intersection, prove that the chords are equal.

Question: In the given figure, AB is a diameter of the circle C (O, r) and the radius OD is perpendicular to AB. If C is any point on arc DB, find ∠ACD and ∠BAD.

circle-question-5

Question: Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord.

Question: D is a point on the circumcircle of ABC in which AB = AC such that B and D are on opposite sides of line AC. If CD is produced to a point E such that CE = BD, prove that AD = AE.

Question: Prove that the quadrilateral formed (if possible) by the internal angle bisectors of any quadrilateral is cyclic.

Question: If PAB is a secant to a circle intersecting the circle at A and B and PT is a tangent segment then Prove that PA.PB = PT2.

Question: Prove that the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

Related: Quantitative Aptitude: Questions

Question: Let ABC be a triangle, AD the altitude through A and AK the circumdiameter through A. Then prove that ∠DAK = ∠B – ∠C. And also the angular bisector AX of A bisects ∠DAK.

Question: In given figure, ∠ABC = 69o, ∠ACB = 31o, find ∠BDC.

Question: If S is the circumcentre of a △ABC, AS meets BC at M meets CA at N and CS meets AB at P, Prove that 1/AM + 1/BN + 1/CP = 2/R, where R is the circum-radius.

Question: Three girls Ruchika, Sonika and Monika are playing a game by standing on a circle of radius 5 m drawn in a park. Ruchika throws a ball to Sonika, Sonika to Monika, Monika to Ruchika. If the distance between Ruchika and Sonika and between Sonika and Monika is 6 m each, what is the distance between Ruchika and Monika?

Question: If the non-parallel sides of a trapezium are equal, prove that it is cyclic.

Question: Find the length of a chord which is at a distance of 8 cm from the centre of a circle of radius 17 cm.

Question: If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes equal angles with the chords.

Also Download: class 9th Circles Objective practice questions

Share with your Friends...
Share on Facebook
Facebook
Tweet about this on Twitter
Twitter
Share on LinkedIn
Linkedin
Pin on Pinterest
Pinterest
Print this page
Print

About the author

Vishal Arora

Leave a Comment

2 Comments