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Q.1. Protve that the line forcing thecentre of two intre secting cicleis the perpendicular besector of theline joing the points ofintursection. |
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Answer» <P>Step-by-step explanation: Let A and B be CENTRES of two circles intersecting at POINTS P and Q. In △APB and △AQB, AP=AQ∵They are radii of a circle. BP=BQ∵They are radii of a circle. AB=AB∵COMMON side △APB≅△AQB By S.S.S. Criterion ⇒∠PAB=∠QAB By C.P.C.T.C. Now, In △APR and △AQR AP=AQ∵ They are radii of a circle. ∠PAR=∠QAR∵∠PAB=∠QAB AR=AR∵ Common side △APR≅△AQR ....... By S.A.S. Criterion ⇒PR=RQ ..... By CPCT And ∠ARP=∠ARQ ....... By C.P.C.T.C. Also, ∠ARP+∠ARQ=180 o ∵ PQ is a straight line. ⇒∠ARP+∠ARP=180 o
⇒2×∠ARP=180 o
⇒∠ARP= 2 180 o
=90 o
Thus, AB⊥ r PQ |
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