Point Z is the incenter of triangle RST. What is the value of x?
x = 2, x = 3, x = 5, x = 8

Incenter of the Triangle RST

Solution:

Given, In △RST.

Z is the incenter of △RST.

Let AS, RB, CT are the three perpendicular bisectors.

In △SAZ and △SBZ

AZ = BZ (Z is the center)

∠SAZ = ∠SBZ (perpendicular bisector)

SZ = SZ (common)

△SAZ ≅ △SBZ (RHS congruence criteria)

∠ASZ = ∠BSZ (CPCT)

5x - 9 = 16

5x = 16 + 9

5x = 25

x = 5.

Point Z is the incenter of triangle RST. What is the value of x?

Summary:

If point Z is the incenter of triangle RST. The value of x = 5.

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