Question

PLEASE HELP IT IS VERY URGENT!!

Please help to find (b) (c) (d)
(b) is in the picture

(c) Given that the ratio of PL to LF is 2 : 3, find the ratio of the area of triangle PLM to the area of triangle PFG.

(d) A circle is drawn by using FG as the diameter. Explain if the point M lies on the circumference of this circle.​

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Answer 1

Explanation:

(c)

`In\: \triangle PLM \: \&\: \triangle PLM\\</p><p>\angle PLM \cong\triangle PFG.. (corresponding \:\angle s) \\</p><p>\angle LPM \cong \angle FPG.. (common \: \angle s) \\</p><p>\therefore \triangle PLM\sim\triangle PFG.. (by\: AA\:Postulate) \\</p><p>PF = PL + LF = 2 + 3 = 5`

By area of similar triangle theorem:

`\frac {A(\triangle PLM)}{A(\triangle PFG)}= (PL^2)/(PF^2)\\</p><p>\therefore \frac {A(\triangle PLM)}{A(\triangle PFG)}= (2^2)/(5^2)\\</p><p>\therefore \frac {A(\triangle PLM)}{A(\triangle PFG)}= (4)/(25)\\</p><p>A(\triangle PLM)\: :\: A(\triangle PFG) = 4 \: :\: 25</p><p>`