Homework Help: circle inscribed

Posted by lilman on Tuesday, May 22, 2012 at 7:04pm.

--------------- QUESTION FOLLOWS --------------------------
Can someone Please help I definitely do not know how to do this.

A)Find x, to find x you need to add the arc measures together and set the expression equal to the total degrees of circle then solve for X, must show all steps.
B)Is the triangle equilateral, isosceles, or scalene, explain, plug your x-value from A into each of the arc measures to find what each arc measures.
Apply the Inscribed Angles Theorem to find <P, <R, <S.
Use the angle measure from step 2 above to determine what type of triangle you have.

The picture is a circle with a triangle inside, QP=(8x-10) and PR=(6x), and QR=(10x+10) QP and PR are the sides and QR is the bottom.
Sure hope someone can help.

circle inscribed - Reiny, Tuesday, May 22, 2012 at 8:48pm
According to the wording of part a) your description of
QP= 8x-10, PR = 6x etc
must have said
arc QP = 8x-10 etc

so 8x-10 + 6x + 10x+10 = 360
24x = 360
x = 15
so arc QP = 8(15) - 10 = 110°
PR = 90°
QR = 160°

By the inscribed angle theorem, the angle opposite the arc must be half the central angle subtended by the arc. Then....

angle R = 55°
angle Q =45°
angle P = 80°

looks like plain old scalene triangle

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