Question : Two points P and Q are 3 cm apart. These two points lie on the circumference of a circle having a radius of 1.7 cm. What is the distance (in cm ) of the line segment PQ from the centre of the circle?
Option 1: 0.8
Option 2: 1.0
Option 3: 0.4
Option 4: 0.6

Question

Question : The distance between the centres of two circles of radii 3 cm and 8 cm is 13 cm. If the points of contact of a direct common tangent to the circles are P and Q, then the length of the line segment PQ is:
Option 1: 11.9 cm
Option 2: 12 cm
Option 3: 11.58 cm
Option 4: 11.5 cm

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Answer 1

Correct Answer: 0.8

Solution :
Let O be the centre of the circle of radius 1.7 cm which is drawn to pass through P and Q. From O draw OR $⊥$ PQ.
Then OR is the required distance.
⇒ PR = QR = $\frac{3}{2}$ = 1.5 cm (perpendicular from centre bisects chord)
Now, In right-angled $△$ ORQ,
Applying Pythagoras theorem,
$O Q^{2} = O R^{2} + Q R^{2}$
⇒ $O R^{2} = (1.7)^{2} - (1.5)^{2}$
⇒ $O R^{2} = 2.89 - 2.25$
⇒ $O R^{2} = 0.64$
⇒ $O R = \sqrt{0.64}$
⇒ $O R = 0.8 cm$
Hence, the correct answer is 0.8.

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Question : Two points P and Q are 3 cm apart. These two points lie on the circumference of a circle having a radius of 1.7 cm. What is the distance (in cm ) of the line segment PQ from the centre of the circle?Option 1: 0.8Option 2: 1.0Option 3: 0.4Option 4: 0.6

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Question : Two points P and Q are 3 cm apart. These two points lie on the circumference of a circle having a radius of 1.7 cm. What is the distance (in cm ) of the line segment PQ from the centre of the circle?
Option 1: 0.8
Option 2: 1.0
Option 3: 0.4
Option 4: 0.6