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10th Class Mathematics Chapter 9 Test10th Class · Mathematics · Punjab (PTB)
Q1. Multiple choice questions (Attempt all · 10 × 1 = 10)
Any two angles in the same segment of the circle are:
An angle in a segment greater than a semicircle is ...... angle:
If r=6cm and
radians, then arc length is:
...... tangents can be drawn to a circle from a point outside the circle:
Which is the formula of area of a sector of a circle:
In circle, radius and tangent are:
The radii of two circles are 15cm, 9cm. what is the distance between their centres they touch internally:
Find the radius of a sector with an area of 50 units and Q is 4 radians:
If
is the radial sagmen in a circle,
is a tangent, them:
A circular running track subtends angle of
at the centre. What angle does it subtend at a point on the boundary:
Q2. Short questions (Attempt any 6 of 8 · 6 × 2 = 12)
An architect designs a circular dome on a building. A lighting rod is placed 12 m away from the centre of the dome which has a radius of 5m. Support cables are attached from the rod to the dome, touching the dome at two points. What is the length of each cable?
Find
, when:
Find the angles marked in the given figure, where O is the centre of the circle.

S,T,U and V are points on the circumference of a circle. Find the angles x and y.
Find the angles x and y in the following figure:

A small sensor lies insida a satellite dish and touches its wall internally. If the dish has radius 15 cm and the sensor has radius 2.5 cm, find the distance between their centres.
Define the tangent to a circle.
D,F and F are point on the circumference of a circle with centre at O and
. Find
.

Q3. Long questions (Attempt any 2 of 3 · 2 × 4 = 8)
A pyramid-shaped sculpture is placed in the center of a circular plaza with a radius of 10m. A decoractive pole stands 26 m from the center of the circle. Two guide wires are attached from the pole to the plaza edge, just touching the circle. Find the length of each wire.
In a historical monument, a cirular fountain with a radius of 3 m is built. A flagpole is erected 7m away from the centre of the fountain. Two ropes from the pole are tied to the edge of the foutain, just touching it. Find the length of each rope.
A sector cut from a circle of radius 5cm has a perimeter of 16cm. Find the area of this sector.