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CBSE Class 10 Answered

In the adjoing figure p and q are points on the sides AB and AC respectively of triange ABC such that AP=3.5 CM PB- 7CNM AQ=3CM AND QC= 6CM PROVE THAT PQ // BC. FIND THE RATION IN WHICH P(4,M) divides the line segments joining the points A(2,3) AND B (6,3) FIND M.   WITHOUT USING TRIGONOMETRIC TABLES EVALUATE THE FOLLOWING SIN 18 DEGREE /COS 73 DEGREE + CUBE 3 ( TAN 10 DEGREE TAN 30 DEGREE TAN 40 DEGREE TAN 50 DEGREE TAN 80 DEGREE)\  
Asked by venugopal.a.madathil | 17 Feb, 2019, 16:54: PM
answered-by-expert Expert Answer
From figure, it can be seen that PQ divides the sides AB and AC in same ratio 1:2.
If a line passing through two sides of the triangle divides these two sides in same ratio, then the line is parallel to th e third side of triangle
 
Hence PQ || BC
----------------------------------------------
 
Let the point P(4,m) divides the line joining the points A(2,3) and B(6,3) in the rato k:1
 
Then x-coordinate of P is given by begin mathsize 12px style fraction numerator 6 k plus 2 over denominator k plus 1 end fraction space equals space 4 end style  ;  solving for k, we get k = 1
Hence P is mid point of A and B.
 
m = (3+3)/2 = 3
Answered by Thiyagarajan K | 17 Feb, 2019, 17:32: PM

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