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6. The 4th term of an A P is zero. Prove that the 25th term ot the Al I37. ABC is a triangle. A circle touches sides AB and AC produced and side BC at X, Y and Z respectively.Show, that AX-_ perimeter of AABC. |
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Answer» From the figure u will get thatAX=AYBX=BZCY=CZnowper of triangle ABC =ab+bc+ac=ab+(bz+zc)+ac=ab+bx+ac+cy=ax+ay=2axper of triangle ABC =2axtherefore1/2perimeter of triangle =ax . 7)Tangents from an exterior point to a circle are equal in length.∴ BP = BQ ----- -(i) CP = CR ------(ii) and, AQ = AR ----- (iii)AQ = AR⇒ AB + BQ = AC + CR⇒ AB + BP = AC + CP...(iv) [From eqn (i) and eqn (ii)]Perimeter of ΔABC= AB + BC + AC= AB + (BP + PC) + AC= (AB + BP) + (AC + PC)= 2(AB + BP) [From eqn (iv)]= 2 AQ [From eqn (i)]⇒ AQ = 1/2(Perimeter of ΔABC) |
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