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
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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 $\perp$ PQ. Then OR is the required distance. ⇒ PR = QR = $\frac{3}{2}$ = 1.5 cm (perpendicular from centre bisects chord) Now, In right-angled $\triangle$ORQ, Applying Pythagoras theorem, $OQ^2=OR^2+QR^2$ ⇒ $OR^2=(1.7)^2 – (1.5)^2$ ⇒ $OR^2=2.89-2.25$ ⇒ $OR^2=0.64$ ⇒ $OR=\sqrt{0.64}$ ⇒ $OR = 0.8\ \text{cm}$ Hence, the correct answer is 0.8.
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