Most circle geometry questions I understand, but these are from my homework that I don't understand.
Thanks for your help.
Hello, skitty!
Here's the first one . . .
[quote]1. Prove that the triangles in the diagram are both right triangles.Code:Q o * * * * * * * * * * * * * * * * * P o * * * * * * * * * o R * * * * * * * * * * * * * * * o * * S
We are given: .
Since
Then: .[1]
And: .[2]
Add [1] and [2]: .
. . That is: .
Since , then: .
Since are inscribed in semicircles,
HELLO SKITTY
ANSWER TO SECOND QUESTION
TO PROVE-
PERIMETER (PQR)=2PA
PROOF-
PA=PB (Tangents from external point)
Also;
QX=BQ and AR=RX (Tangents from external point)
now;
PQ+QX=PR+XR
PQ+QX+PR+XR=PERIMETER(PQR)
2(PR+RX)=Perimeter(PQR)
2PA=Perimeter (PQR)
hence proved.
hello skitty;
answer to fourth question-
TO PROVE-
angle QOS=90
PROOF-
anglePQS+angleRSQ=180 (CO-INTERIOR ANGLES)
anglePQO=angleSQO and angleRSO=angleQSO
NOW;
1/2 (anglePQS+angleRSQ)=90
angleSQO+angleQSO=90
BY ANGLE SUM PROPERTY OF TRIANGLE-
angleSQO+angleQSO+ angleQOS=180
angleQOS=180-90=90
So angleQOS=90
HENCE PROVED