TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110°

Question

If TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110°, then ∠PTQ is equal to

My attempt:

$P$ and $Q$ are $90°$ each – Raffaele Feb 05 '21 at 14:33 — Raffaele, Feb 05 '21 at 14:33

score 0 · Accepted Answer · answered Feb 05 '21 at 14:34

0

$ OP ⊥ PT and TQ ⊥ OQ $

$ ∴∠OPT = ∠OQT = 90° $

Now, in the quadrilateral POQT, we know that the sum of the interior angles is 360°

So, $ ∠PTQ+∠POQ+∠OPT+∠OQT = 360° $

Now, by putting the respective values we get,

$ ∠PTQ +90°+110°+90° = 360° $

$ ∠PTQ = 70° $

answered Feb 05 '21 at 14:34

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