Question

in figure, o is the center of circle, PQ is a chord and PT is a tangent at P. If angle POQ=70deg, find angle TPQ.

Answer 1

Given÷o is the centre of the circle.PQ is a chord
PT is a tangent
anglee POQ=70
To prove÷Find TPQ
Proof÷In triangle OPQ
Let angle OPQ and PQO will be k
by angle sum property
OPQ+PQO+POQ=180
k+k+70=180
2k=180-70
2k=110
k=110/2
k=55
angle OPQ and PQO=55
TPO=90 (angle drawn on the tangent is of 90degree)
TPQ+OPQ=90 (TPO=TPQ+OPQ)
TPQ+55=90
TPQ=90-55
TPQ=35degrees

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Answer 2

in figure, o is the center of circle, PQ is a chord and PT is a tangent at P. If angle POQ=70deg, find angle TPQ.
Given÷o is the centre of the circle.PQ is a chord
PT is a tangent
anglee POQ=70
To prove÷Find TPQ
Proof÷In triangle OPQ
Let angle OPQ and PQO will be k
by angle sum property
OPQ+PQO+POQ=180
k+k+70=180
2k=180-70
2k=110
k=110/2
k=55
angle OPQ and PQO=55
TPO=90 (angle drawn on the tangent is of 90degree)