In figure below P, Q, R are the points where the incircle of $Δ A B C$ touches the sides. Find $∠ A Q R .$

$80^{\circ}$

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$45^{\circ}$

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$70^{\circ}$

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$180^{\circ}$

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Solution

The correct option is C
$70^{\circ}$

Since, AQ and AR are the tangents to the circle

So, AQ = AR (tangents drawn from same point).

$∠ A Q R = ∠ A R Q$ (angles opposite to equal sides)

So, In $Δ A Q R$

$∠ A Q R + ∠ A R Q + 40 = 180^{\circ}$

$2 ∠ A Q R = 140$

$∠ A Q R = 70^{\circ}$

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In figure below P, Q, R are the points where the incircle of ΔABC touches the sides. Find ∠AQR.

The correct option is C 70∘ Since, AQ and AR are the tangents to the circle So, AQ = AR (tangents drawn from same point). ∠AQR=∠ARQ (angles opposite to equal sides) So, In ΔAQR ∠AQR+∠ARQ+40=180∘ 2∠AQR=140 ∠AQR=70∘

In figure below P, Q, R are the points where the incircle of $Δ A B C$ touches the sides. Find $∠ A Q R .$