Q3 of 59 Page 63

In fig 3.39 chord AB ≅ chord CD, Prove that, arc AC ≅ arc BD


∵ chord AB ≅ chord CD


∴ m(arc AB) = m(arc CD){Corresponding arcs of congruent chords of a circle (or congruent circles) are congruent}


Subtract m(arc CB) from above,


m(arc AB)– m(arc CB) = m(arc CD) – m(arc CB)


⇒m(arc AC) = m(arc BD)


⇒arc AC ≅ arc BD


Hence, proved.


More from this chapter

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1

In figure 3.37, points G, D, E, F are concyclic points of a circle with centre C.

∠ ECF = 70°, m(arc DGF) = 200° find m(arc DE) and m(arc DEF).



 2

In fig 3.38 ∆ QRS is an equilateral triangle. Prove that,

(1) arc RS ≅ arc QS ≅ arc QR


(2) m(arc QRS) = 240°.



 1

In figure 3.56, in a circle with centre O, length of chord AB is equal to the radius of the circle. Find measure of each of the following.


(1) ∠ AOB (2) ∠ ACB


(3) arc AB (4) arc ACB.


 2

In figure 3.57, is cyclic. side PQ ≅ side RQ. ∠ PSR = 110°, Find-


(1) measure of ∠ PQR


(2) m(arc PQR)


(3) m(arc QR)


(4) measure of ∠ PRQ