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 Side Ratio Resolution (Posted on 2015-07-18)
Triangle PQR has incentre I and circumcentre O. Suppose that ∠ PIO = 90o and ∠ QIO = 45o.

Find the ratio PQ: QR : RP

 No Solution Yet Submitted by K Sengupta No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 re(2): Solution | Comment 3 of 4 |
(In reply to re: Solution by Jer)

I don't know if this construction
will help you with a proof for the
problem.

Geometer's Sketchpad Construction:

1. Construct a fixed segment IP.

2. Construct line m through I
perpendicular to IP.

3. Construct point O on line m.

4. Construct ray IE such that
angle PIQ = 135 degrees and
point O lies in its interior.

5. Construct circle C with center O
and passing through point P.

6. Point Q is the intersection of
circle C and ray IE.

7. Reflect line PQ about IP to
get line PS.

8. Reflect line PQ about IQ to
get line PT.

9. Point R is the intersection of
PS and PT ( Note angle PRQ is
90 degrees ).

10. Note as point O moves on line m
that point R is inside circle C
when O is inside triangle PQR
and point R is outside circle C
when O is outside triangle PQR.

R lies on circle C when O is
the midpoint of segment PQ.

 Posted by Bractals on 2015-07-20 17:27:26
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