Hi there! Have questions about your homework? At Brainly, there are 60 million students who want to help each other learn. Questions are usually answered in less than 10 minutes. Try it for yourself by posting a question! :D

Hi there! Have questions about your homework? At Brainly, there are 60 million students who want to help each other learn. Questions are usually answered in less than 10 minutes. Try it for yourself by posting a question! :D

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

See diagram.

AQ = AR = lengths of tangents from point A to the ex-circle of triangle ABC. BQ = BP = lengths tangents from B onto the excircle. CR = CP = lengths of tangents from C onto the excircle. AQ = AB + BQ = AB + BP AR = AQ = AC + CR = AC + CP AQ + AR = 2 AQ = AB + BP + PC + CA = perimeter of triangle ABC So perimeter = 2 * 5 cm = 10 cm =================================== 2) 6 + 6 + 6 + .... n terms = 6 * n

3) (xb - c) /bc + (xc -a )/ca + (xa - b) / ab = [ ax b - ac + x bc - ab + xac - bc ] / abc = (x - 1) ( ab + bc + ca) / abc 4) case 1) perimeter of the sector exceeds the diameter by 16.8 cm (2 R + arc length) - 2 R = 16.8 cm => arc length = 16.8 cm

case 2) arc length exceeds R Ф - 2 R = 16.8 cm. there are two parameters R & Ф. we need more information to solve this. ================== 5) T3 = 5 = a + 2 d T7 = a + 8 d = 9 subtract equations, 6 d = 4 => d = 2/3 => a = 11/3 ===================== 6) In a cyclic quadrilateral, sum of opposite angles is 180 deg. Cos A + Cos C = 2 Cos (A+C)/2 Cos (A-C)/2 = 0 As (A+C)/2 = 90 deg similarly Cos B + Cos D = 0 as (B+D)/2 = 90 deg. hence the answer is 0. ======================= 7) tan 1 tan2 tan 3 ...... tan 88 tan 89 = tan1 tan2 tan 3 .... tan 43 tan 44 tan 45 cot 44 cot 43 .... cot 3 cot 2 cot 1 = tan 1 cot 1 tan 2 cot2 tan3 cot3 .... tan43 cot43 tan44 cot44 * 1 = 1 Log 1 = 0 ============== 8) x / 5 , x/4 x/3 , x/2 median is the average of x/4 and x/3 so x/4 + x/3 = 2 * 8 = 16 7 x / 12 = 16 x = 12 * 16 / 7 ====================== 9) D = discriminant = b² (c-a)² - 4 ac (b-c) (a-b) = b² (c² + a² - 2 a c) - 4 a c ( a b - b² - a c + b c) = b² c² + a² b² - 2 a c b² - 4 a² b c + 4 a c b² + 4 a² c² - 4 a b c² = b² c² + a² b² + 2 a c b² - 4 a² b c + 4 a² c² - 4 a b c² = b² (a +c)² - 4 a c (a b - a c + b c) = (a+c)² [ b² - 4 abc ] + 4 a² c²