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Class 9th CIRCLE CBSE TEST PAPER

I. Fill in the blanks.

a. The word tangent comes from the Latin word ------------

b. A tangent to a circle intersects it in ----------- point (s).

c. A line intersecting a circle in two points is called a --------

d. A circle can have -----------parallel tangents at the most.

e. The common point of a tangent to a circle and the circle is called ----------

2. Solve these questions (any five) 4X5=20

i. Prove that The tangent at any point of a circle is perpendicular to the radius through the point

of contact

ii. Prove that the lengths of tangents drawn from an external point to a circle are equal.

iii. Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove

that < PTQ =2 < OPQ.

Fig.1 fig.2

iv. PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a

point T (see Fig. 2) Find the length TP.

v. Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary

angles at the centre of the circle.

vi. Prove that the angle between the two tangents drawn from an external point to a circle is

supplementary to the angle subtended by the line-segment joining the points of contact at the

centre.

vii. The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm.

Find the radius of the circle.