ICSE Board Practice

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ICSE Grade X - Tangent Properties of Circles

Question 1

1.	In the given figure, GHIJ is a cyclic quadrilateral such that IG bisects ∠JGH and KL is the tangent at I. If ∠IGH = 53°, find ∠KIH
	68° 58° 83° 63° 53°

Question 2

2.	If two circles touch externally , the number of their common tangents is
	2 5 1 4 3

Question 3

3.	In the given figure, O is the centre of the circle and the tangents HK and JK meet at point K. If ∠IJH = 59°, find ∠JKH
	92° 67° 77° 72° 62°

Question 4

4.	In the given figure, IG and IH are tangent segments to the circle with centre O. Given ∠HIJ = 27°, find ∠GHJ
	61.5° 46.5° 41.5° 31.5° 36.5°

Question 5

5.	In the given figure, O is the centre of the circle and IJ is the tangent at H. If ∠HFG = 42°, find ∠IHG
	72° 52° 57° 47° 42°

Question 6

6.	Which of the following statements are true?
	a) Two semi-circles of a circle together make the whole circle. b) An infinite number of chords may be drawn for a circle. c) One and only one tangent can be drawn to a circle from a point outside it. d) Every circle has a unique diameter. e) An infinite number of diameters may be drawn for a circle.
	{d,b} {a,b,e} {c,a} {c,d,e} {c,a,b}

Question 7

7.	In the given figure, DB and DC are tangent segments to the circle with centre O. Given ∠CDE = 37°, find ∠BCO
	52° 67° 37° 47° 42°

Question 8

8.	In the given figure, O is the centre of the circle and FG is the tangent at C. If ∠ODC = 37°, find ∠GCD
	58° 53° 83° 63° 68°

Question 9

9.	In the given figure, two circles intersect at points K & L. A tangent is drawn at point M. From the same point, two lines are drawn passing through points K & L. They meet the other end of the second circle at J & I. Given ∠M = 84°, find ∠JIL
	84° 94° 99° 89° 114°

Question 10

10.	In the given figure, CD and EF are parallel tangents to the circle with centre O. CF is another tangent meeting CD and EF at C and F. Find ∠COF
	120° 90° 105° 95° 100°

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