In the diagram, TP and TQ are tangents to the circle at the point P and Q respectively. TQY is a straight line. Given that ∠RPQ = 26°, ∠SQY = 42° and ∠RXQ = 101°, calculate the following angles.
(a) ∠QRS
(b) ∠RQP
(c) ∠RQS
(d) ∠PTQ
In the diagram, TP and TQ are tangents to the circle at the point P and Q respectively. TQY is a straight line. Given that ∠RPQ = 26°, ∠SQY = 42° and ∠RXQ = 101°, calculate the following angles.
(a) ∠QRS
(b) ∠RQP
(c) ∠RQS
(d) ∠PTQ
Hello PunchDo you know the Alternate Segment Theorem? This gives:
(a)
(b) can then be calculated from the angles of .
(c) Using the alternate segment theorem again, . So you can now find from the straight line .
(d) (since is isosceles). So you can now work out .
Can you fill in the gaps?
Grandad
as I can see you find most angles but you can find all of them by finding QPS
there is a theorem said that the angle between the tangent of the cirlce and the chord equal to the angle on that chord so
QPS=SQY = 42
I think now you can find all
you can use this to find RQT and RPT
RQT = QSR
RPT = RSP