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Maths 1 Marks Question

Circles · Jharkhand Board (JAC) STD 10 (Jharkhand - English Medium). 8 questions.

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Question 11 Mark
If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 80°, $\angle$POA is equal to
Answer
Here $\angle $APB = 80°
$\therefore $$\angle $AOB = 180° - 80° = 180°
Now, since OP bisect $\angle $APB and $\angle $AOB.
$\therefore $$\angle $AOP = $\frac{{{{100}^ \circ }}}{2} = {50^ \circ }$
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Question 21 Mark
From a point Q, the length of tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is
Answer


Here $\angle O P Q=90^{\circ}$ [Tangent makes right angle with the radius at the point of contact] in right angled triangle OPQ
$\therefore O Q^2=O P^2+P Q^2 \Rightarrow(25)^2=O P^2+(24)^2$
$\Rightarrow O P^2=625-576$
$\Rightarrow O P=7 cm$ Therefore, the radius of the circle is 7 cm
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Question 31 Mark
A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is:
Answer
We know that the line drawn from the centre of the circle to the tangent is perpendicular to the tangent.
$OP \perp PQ$
By applying Pythagoras theorem in ΔOPQ,

$OP^2 + PQ^2 = OQ^2$
$5^2 + PQ^2 =12^2$
$PQ^2 =144 - 25$
$\mathrm{PQ}=\sqrt{119} \mathrm{cm}$
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Question 81 Mark
How many tangents can a circle have?
Answer
A circle can have infinitely many tangents since there are infinitely many points on the circumference of the circle and at each point of it, it has a unique tangent.
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