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CBSE Class 10- Mathematics: Questions and Answers Chapter β 10 Circles Part 16
Question 14:
Prove that the lengths of two tangents drawn from an external point to a circle are equal.
Answer:
Given: P is an external point to the circle .
and PR are two tangents from P to the circle.
To Prove:
Construction: Join
Proof:
A tangent to a circle is perpendicular to the radius through the point of contact
Now in right triangles and ,
[Each radius r]
Hypotenuse. Hypotenuse. OP [common]
Question 15:
The circle of touches the sides BC, CA, and AB at D, and F, respectively. If , prove that .
Answer:
Tangents drawn from an external point to a circle are equal in length
[Tangents from A] β¦ (i)
[Tangents from B] β¦ (ii)
[Tangents from C] β¦ (iii)
Adding (i) , (ii) and (iii) , we get
But
Question 16:
A circle touches the side BC of a at point P and touches AB and AC when produced at Q and R respectively, show that AQ [Perimeter of ] .
Answer:
Since the tangents from an external point to a circle are equal in length,
β¦ (i) [from point B]
β¦ (ii) [from point C]
And β¦ (iii) [From point A]
From (iii) , we have
[Using (i) and (ii) ]
Now perimeter of
[using (iv) ]
[using (i) ]