In the given figure, PAQ and PBR are tangents to the circle with centre 'O' at the points A and B respectively. If ∠…

CBSE Class 10 Maths PYQ · Circles · Find angles · 2 Marks · March 2024 · Standard

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592 Marks · March 2024 · Standard
In the given figure, PAQ and PBR are tangents to the circle with centre 'O' at the points A and B respectively. If $\angle QAT = 45^\circ$ and $\angle TBR = 65^\circ$, then find $\angle ATB$.
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Join OA, OB and OT
Now $\angle ATO = \angle TAO = 90^\circ - 45 = 45^\circ$
and $\angle BTO = \angle TBO = 90^\circ - 65^\circ = 25^\circ$
$\Rightarrow \angle ATB = \angle ATO + \angle BTO$
$= 45^\circ + 25^\circ = 70^\circ$
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