28. Required fig. 1 Since, tangents from an external point to a circle are equal in length 1 BP = BQ -----------(i) CP = CR -----------(ii) And, AQ =AR -----------(iii) or, AB + BQ = AC + CR 1 or, AB + BP = AC + CP Now, Perimeter of 1 = AB + ( BP +PC) + AC = (AB + BP) + (AC +PC) = 2 (AB+BP) = 2(AB+BQ) = 2AQ Proved. Or Required fig. 1 We know that the tangents to a circle from an external point are equal in length. 1 --------------(i) BP = BQ -------------(ii) CR = CQ ------------(iii) DR =DS ------------(iv) Adding (i), (ii), (iii) & (iv), we get 1 (AP+BP) + (CR+DR)= (AS+DS) + (BQ+CQ) or, AB + CD = AD +BC or, 2AB = 2BC 1 or, AB = BC so, AB = BC = CD = AD ABCD is a rhombus. Proved. 29. For correct fig. 1 1 Let AB = Building, CD = Tower In, tan300= or, In, 1 tan600= or, = -------------(ii) By (i) & (ii) 1
28. Required fig. 1 Since, tangents from an external point to a circle are equal in length BP = BQ -----------(i) CP = CR -----------(ii) And, AQ =AR -----------(iii) 1 or, AB + BQ = AC + CR or, AB + BP = AC + CP 1 Now, Perimeter of = AB + ( BP +PC) + AC = (AB + BP) + (AC +PC) = 2 (AB+BP) = 2(AB+BQ) = 2AQ Proved. 1 Or Required fig. 1 We know that the tangents to a circle from an external point are equal in length. --------------(i) BP = BQ -------------(ii) CR = CQ ------------(iii) DR =DS ------------(iv) 1 Adding (i), (ii), (iii) & (iv), we get (AP+BP) + (CR+DR)= (AS+DS) + (BQ+CQ) or, AB + CD = AD +BC 1 or, 2AB = 2BC or, AB = BC so, AB = BC = CD = AD ABCD is a rhombus. Proved. 1 29. For correct fig. Let AB = Building, CD = Tower In, tan300= or, 1 1 In, tan600= or, = -------------(ii) 1 By (i) & (ii) 1
1288508582final_study_material_maths_class_x_2012-2013.docx