Two tangents TP and TQ are …
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Sia ? 6 years, 4 months ago
Let {tex}\angle O P Q \text { be } \theta{/tex}
{tex}\therefore \quad \angle T P Q = \left( 90 ^ { \circ } - \theta \right){/tex}
Since TP = TQ (Tangents)
{tex}\therefore \quad \angle T Q P = \left( 90 ^ { \circ } - \theta \right){/tex}
(Opposite angels of equal sides)
Now, {tex}\angle T P Q + \angle T Q P + \angle P T Q{/tex} = 180o
{tex}\Rightarrow 90 ^ { \circ } - \theta + 90 ^ { \circ } - \theta + \angle P T Q{/tex} {tex}= 180 ^ { \circ }{/tex}
{tex}\Rightarrow \quad \angle P T Q = 180 ^ { \circ } - 180 ^ { \circ } + 2 \theta{/tex}
{tex}\Rightarrow \quad \angle P T Q = 2 \theta{/tex}
Hence {tex}\angle P T Q = 2 \angle O P Q{/tex}
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