Former Question
Q.1.PA and PB are tangents from P to
the circle with centre O. At point M, a tangent is drawn cutting PA at K and PB
at N. prove that KN = AK + BN.
Q.2. A circle touches the side BC of a ∆ABC at
P and touches AB and AC produced at Q and R respectively. Prove that AQ=
½(perimeter of ∆ABC)
Q.3 fig 1. XP and XQ are tangents
from X to the circle with centre O. R is a point on the circle . Prove that
XA+AR = XB+BR.
Q.4 All sides of a parallelogram
touches a circle, show that the parallelogram is a rhombus.
Q.5 The radii of the concentric
circles are 13 cm and 8 cm. AB is a diameter of the bigger circle . BD is a
tangent to the smaller circle touching it at D. find the length of AD.
Q.6 BAC is a right angled triangle
right angle at A. A circle is inscribed in it. The lengths of two sides
containing the right angle are 6cm and 8 cm . find the radius of the circle.
Q.7 ABCD is a quadrilateral such
that angle D = 90o. A circle C(O,r) touches the sides AB,BC,CD and
DA at P,Q,R and S respectively if BC=38cm ,CD=25cm and BP=27cm, find r.
Q.8 Prove that the tangents from
extremities of any chord make equal angles with the chord.
Q.9.if PA and PB are two tangents
drawn from a point P to a circle with centre O touching it at A and B
respectively, prove that OP is the perpendicular bisector of AB.
Q.10in fig.2 sides of ∆ABC touch the
circle C(O,r) at P,Q and R. show that (i) AB+CQ = AC + BQ (II) area(OBC)=1/2BC
X r (iii) area(ABC) =1/2(perimeter of ∆ABC) X r
Q.11 QR is atangent at Q to the
circle whose centre is P. PR || AQ, where AQ is a chord through A, the end
point of diameter AB. Prove that BR is a tangent at b
Q.12 in fig. 3 PQ is a chord of
length 8 cm of a circle of radius 5cm . the tangents at P and Q intersect at a
point T. find the length TB.
Q.13 In fig . 4 O is the centre of
the circle, PA and PB are tangent segments, show that (i)PAOB is a cyclic
quadrilateral (ii)PO is the bisector of angle APB(iii)angle OAB = angle OPA.
Q.14 from a point P, the tangents PA
and PB are drawn to a circle with centre O. if OP =diameter of the circle,show
that ∆APB is equilateral.
Q.15 in fig. 5 circle C(O,r) and
C(O`,r\2) touch internally at a point A and AB is a chord of the circle C(O,r)
intersecting C(O`,r\2 ) at C . prove that AC =CB.
Q.16 In the concentric circle, prove
that all chords of the outer circle which touch the inner circle are equal in
length.
Q.17 In fig 6 ∆PAB is formed by
three tangents to a circle with centre O, such that angle APB= 40o.
if OA and OB bisect angle TAB and angle RBA respectively, then find the measure
of angle AOB.
Q.18 in fig 7. o is the centre of
the circumcircle of ∆XYZ.tangents at X and Y intersect at T. given angle XTY =
80o and angle 140o. calculate the value of angle ZXY.
Q.19 in fig 8, two non-intersecting
circle of equal radii have their centres at C1 and C2. If
p lies on the perpendicular bisector of C1C2, show that
the length of the tangents PL and PM are equal.
Q.20 (therom of secent)PAB is a
secant and PT is a tangent.prove that PA X PB = PT2
Answer
5.AD = 19cm 6. 2cm 7.14cm 12. TP=20/3 17. 70o 18. 60o
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