Q4 of 59 Page 55

What is the distance between two parallel tangents of a circle having radius4.5 cm ? Justify your answer.

Let BC and DE be the parallel tangents to a circle centered at A with point of contact O and H respectively. On joining OH, we find OH is the diameter of the circle.∠ BOA = 90° = ∠ DHA {Using tangent-radius theorem which states that a tangent at any point of a circle is perpendicular to the radius at the point of contact.}


Distance between BC and DE = OH


∵ OH is perpendicular to BC and DE.


OH = 2 × 4.5 cm = 9 cm



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2

In the adjoining figure, O is the centre of the circle. From point R, seg RM and seg RN are tangent segments touching the circle at M and N. If (OR) = 10 cm and radius of the circle = 5 cm, then

(1) What is the length of each tangent segment?


(2) What is the measure of ∠MRO?


(3) What is the measure of ∠MRN?



 3

Seg RM and seg RN are tangent segments of a circle with centre O. Prove that seg OR bisects ∠MRN as well as ∠MON.


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Two circles having radii 3.5 cm and 4.8 cm touch each other internally. Find the distance between their centres.

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Two circles of radii 5.5 cm and 4.2 cm touch each other externally. Find the distance between their centres.