ICSE Board Practice

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ICSE Grade X - Tangent Properties of Circles

Question 1

1.	In the given figure, O is the centre of the circle and GH is the tangent at D. If ∠OED = 31.5°, find ∠HDE
	68.5° 73.5° 88.5° 63.5° 58.5°

Question 2

2.	In the given figure, O is the centre of the circle and KL is the tangent at G. If ∠GJI = 45°, find ∠GHI
	145° 140° 165° 135° 150°

Question 3

3.	In the given figure, BP & CP are tangents to the circle with centre O. Given ∠BPC = 47°, find ∠BOC
	133° 163° 143° 148° 138°

Question 4

4.	The distance between the centres of two circles is d . If the radii are r 1 and r 2 , the length of their transverse common tangent is
	None of these √ d 2 + ( r 1   −   r 2 ) 2 √ d 2 + ( r 1   +   r 2 ) 2 √ d 2 − ( r 1   +   r 2 ) 2 √ d 2 − ( r 1   −   r 2 ) 2

Question 5

5.	Two circles with equal radii are
	not similar only similar but not congruent concentric congruent

Question 6

6.	In the given figure, DT & ET are tangents to the circle with centre O. Given ∠T = 46°, find ∠D
	23° 38° 33° 28° 53°

Question 7

7.	Two circles with radii R and r touch internally. If the distance between their centres is d, then
	d > R - r d < R - r d = R - r d < R + r d = R + r

Question 8

8.	In the given figure, O is the centre of the circle and EG is the tangent at F. If ∠DCF = 27°, find ∠DEF + ∠DFE
	93° 68° 73° 78° 63°

Question 9

9.	O is the centre of the circumcircle of △CDE. Tangents at C and D intersect at F. If ∠CFD = 55.18° and ∠COE = 110°, find ∠ECD
	92.59° 77.59° 62.59° 67.59° 72.59°

Question 10

10.	In the given figure, O is the centre of the circle and GH is the tangent at D. If ∠EDF = 41° and ∠GDE = 82°, find ∠DFE
	56° 41° 51° 71° 46°

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