Q3 of 59 Page 83

In figure 3.83, M is the centre of the circle and seg KL is a tangent segment.

If MK = 12, KL = then find -


(1) Radius of the circle.


(2) Measures of ∠ K and ∠ M.



(1) Here LM is the radius of the circle


⇒ ∠KML = 90° 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.


In triangle MLK right-angled at L,


Given MK = 12, KL = 6√3,


MK2 = LM2 + KL2 {Using Pythagoras theorem}


⇒LM2 = 122 -6√32


⇒LM2 = 144 - 108


⇒ LM = √36


⇒ LM = 6 cm


(2)



⇒∠K = 30°


∠ M + ∠ K + ∠ L = 180° {Angle sum property of the triangle}


So, ∠ M = 180° - ∠ K - ∠ L


⇒ ∠ M = 180° - 30° - 90° = 60°


More from this chapter

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1

Four alternative answers for each of the following questions are given. Choose the correct alternative.

Seg XZ is a diameter of a circle. Point Y lies in its interior. How many of the following statements are true?


(i) It is not possible that ∠XYZ is an acute angle.


(ii) ∠ XYZ can’t be a right angle.


(iii) ∠ XYZ is an obtuse angle.


(iv) Can’t make a definite statement for measure of ∠ XYZ.


 2

Line l touches a circle with centre Oat point P. If radius of the circle is 9 cm,answer the following.

(1) What is d(O, P) = ? Why ?


(2) If d(O, Q) = 8 cm, where does thepoint Q lie?


(3) If d(PQ) = 15 cm, How manylocations of point R are line online l ? At what distance will eachof them be from point P?



 4

In figure 3.84, O is the centre of the circle. Seg AB, seg AC are tangent segments. Radius of the circle isr and l(AB) = r , Prove that, is a square.


 5

In figure 3.85, is a parallelogram. It circumscribes the circle with cnetre T. Point E,F, G, H are touching points. If AE = 4.5,EB = 5.5, find AD.