Q3 of 59 Page 55

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


In triangle MOR and triangle NOR,


MR = NR {∵Tangents from same external point are congruent to each other.}


OR = OR {Common}


OM = ON {Radius of the circle}


⇒ ΔMOR ≅ ΔNOR {By SSS}


⇒ ∠ROM = ∠RON


And ∠MRO = ∠NRO {C.P.C.T.}


Hence proved that seg OR bisects ∠MRNas well as ∠MON.


More from this chapter

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1

In the adjoining figure the radius of a circle with centre C is 6 cm, line AB is a tangent at A. Answer the following questions.

(1) What is the measure of ∠CAB ? Why?


(2) What is the distance of point C from line AB? Why?


(3) d(A,B) = 6 cm, find d(B,C).


(4) What is the measure of ∠ABC ? Why?



 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?



 4

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

 1

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