In fig 3.38 QRS is an equilateral triangle. Prove that,
(1)Given QRS is an equilateral triangle, sides are equal in measure.QR = RS = QSarc QR = arc RS = arc QS [Corresponding arcs of congruent chords of a circle are congruent]arc RS arc QS arc QR….(i)Hence proved.(2)m(arc RS)+ m(arc QS)+ m(arc QR) = 360˚ [Measure of a complete circle is 360°]Also from (i) arc […]
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).
Given ECF = 70˚m(arc DGF) = 200˚m(arc EF) = 70˚ [The measure of a minor arc is the measure of its central angle.]m(arc DGF)+m(arc EF)+m(arc DE) = 360˚ [Measure of a complete circle is 360°.]200+70+ m(arc DE) = 360m(arc DE) = 360-(200+70)m(arc DE) = 90˚m(arc DEF) = m(arc DE)+m(arc EF) [Property of sum of measures […]