Q1 of 59 Page 83

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

Points A, B, C are on a circle, such that m(arc AB) = m(arc BC) = 120°. Nopoint, except point B, is common to the arcs. Which is the type of ∆ ABC?


Angle subtended by the arcs at centre = 120°


⇒ Angle subtended by the arc at the remaining part of the circle = 60° {The measure of an inscribed angle is half the measure of the arc intercepted by it.}


∵ Interior angles of the triangle ABC = 60°


∴It is an equilateral triangle.

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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.


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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?