TripodPie21idn
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3. A circle is inscribed in a triangle whose sides are 9 cm, 14, cm and 17 cm. If P
separates the 14 – cm side into segments whose ratio is x : y with x < y,
find the values of x and y.

3 A Circle Is Inscribed In A Triangle Whose Sides Are 9 Cm 14 Cm And 17 Cm If P Separates The 14 Cm Side Into Segments Whose Ratio Is X Y With X Lt Y Find The V class=

Sagot :

EngrJohannidn

[tex] \Large \mathbb{SOLUTION:} [/tex]

[tex] \begin{array}{l} \begin{cases} \: \textsf{Based from the figure,} \\ \: \sf x + y = 14\quad (1) \\ \\ \: \textsf{By Two-Tangent Theorem,} \\ \: \sf 9 - x = 17 - y \implies x - y = -8\quad (2)\end{cases} \\ \\ \textsf{Adding (1) and (2), we get} \\ \\ \sf 2x = 6 \\ \boxed{\sf x = 3\ cm} \\ \\ \textsf{It follows that} \\ \\ \sf y = 14 - x \\ \sf y = 14 - 3 \\ \boxed{\sf y = 11\ cm} \end{array} [/tex]

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