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20 questions · timed · auto-graded

Question 11 Mark
The length of the tangent from an external point P to a circle of radius 5cm is 10 cm. The distance of the point from the centre of the circle is ____________ .
Answer
$\sqrt{125} cm$
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Question 21 Mark
Quadrilateral ABCD is circumscribed to a circle. If AB = 6 cm, BC = 7 cm and CD = 4 cm, then AD = ____________ .
Answer
3 cm
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Question 31 Mark
If PA and PB are two tangents drawn from an external point P to a circle such that PA = 5 cm and $\angle APB = 60^{\circ}$, then the length of chord AB is ____________ .
Answer
5 cm
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Question 41 Mark
PA and PB are two tangents drawn from an external point P to a circle with centre O. If $\angle PBA=65^{\circ}$, then $\angle APB$ = ____________ .
Answer
$50^{\circ}$
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Question 51 Mark
PA and PB are two tangents drawn from an external point P to a circle with centre O. If $\angle PBA = 65^{\circ}$ then $\angle APB$ = ____________ .
Answer
$50^{\circ}$
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Question 61 Mark
The angle between two tangents drawn from an external point to a circle is ____________ to the angle subtended by the line segments joining the points of contact at the centre.
Answer
supplementary
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Question 71 Mark
If a number of circles pass through the end points P and Q of a line segment PQ, then their centres lie on the perpendicular bisector of ____________ .
Answer
PQ
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Question 81 Mark
If the angle between two tangents drawn from a point P to a circle of radius a and centre O is $60^{\circ}$, then OP = ____________ .
Answer
2a
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Question 91 Mark
The length of the tangent from an external point P on the circle with centre O is always ____________ OP.
Answer
less than
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Question 101 Mark
If a chord AB subtends an angle of 60º at the centre of a circle, then the angle between the tangents at A and B is ____________ .
Answer
$120^{\circ}$
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Question 111 Mark
AB is a diameter of a circle and AC is its chord such that $\angle BAC=30^{\circ}$. If the tangent at C intersects AB extended at D, then BC = ____________ .
Answer
BD
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Question 121 Mark
If angle between two tangents drawn from a point P to a circle of radius a and centre O is $90^{\circ}$ then OP = ____________ .
Answer
$a \sqrt{2}$
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Question 131 Mark
From an external point P, two tangents PA and PB are drawn to the circle with centre O. Then the angle between OP and AB is ____________ .
Answer
$90^{\circ}$
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Question 161 Mark
Tangents drawn from an external point to a circle subtend ____________ angles to the centre.
Answer
equal
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Question 171 Mark
The two tangents drawn from an external point to a circle are ____________ to the segment joining the centre to the point.
Answer
equally inclined
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Fill In The Blanks[1 Marks ] - Maths STD 10 Questions - Vidyadip