IN the given figure,if PQR is a tangent to the circle at q. whose centre is O and AB is a chord parallel to pr such that $∠ B Q R = 70^{o}$ , then find $∠ A Q B$

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Solution

As OQ $⊥$ PR
(radius $⊥$ tangent) & AB $| |$ PR
$\Rightarrow A B ⊥ O L$
and perpendicular from centre to chord bisects the chord.
$\Rightarrow A L = B L$ ,
$∠ Q L B = ∠ Q L A$
& $L Q = L Q$ \Rightarro$ By SAS
congruency, $Δ Q L A ≅ Δ Q L B$
$\Rightarrow ∠ A Q L = ∠ B Q L = 20^{o}$ $(90^{o} - 70^{o})$
$\Rightarrow ∠ A Q B = 40^{o}$ .

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Similar questions

In the given figure, PQR is a tangent to the circle at Q, whose centre is O and AB is a chord parallel to PR such that $∠$ BQR = $70^{o}$ , Then $∠$ AQB = ?

(a) $20^{o}$ (b) $35^{o}$ (c) $40^{o}$ (d) $45^{o}$

Q. In figure if PQR is tangent to circle at Q whose centre is O. AB is a chord parallel to PR and

∠ B Q R = 70^{\circ}

then

∠ A Q B

is equal to

Q. In figure, if PQR is tangent to a circle at Q whose centre is O, AB is a chord parallel to PR and

∠ B Q R = 70^{\circ}

, then

∠ A Q B

is equal to:

Q. In figure. If PQR is the tangent to a circle at Q whose centre is O, AB is a chord parallel to PR and

∠ B Q R = 70^{\circ}

, then

∠

AQB is equal to

Q. In the given figure, PQR is a tangent to the circle at Q, whose centre is O and AB is a chord parallel to PR, such that ∠BQR = 70°. Then, ∠AQB = ?

(a) 20°
(b) 35°
(c) 40°
(d) 45°

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IN the given figure,if PQR is a tangent to the circle at q. whose centre is O and AB is a chord parallel to pr such that ∠BQR=70o, then find ∠AQB

As OQ⊥ PR(radius ⊥ tangent) & AB||PR⇒AB⊥OLand perpendicular from centre to chord bisects the chord.⇒AL=BL,∠QLB=∠QLA& LQ=LQ\Rightarro$ By SAScongruency, ΔQLA≅ΔQLB⇒∠AQL=∠BQL=20o (90o−70o)⇒∠AQB=40o.

IN the given figure,if PQR is a tangent to the circle at q. whose centre is O and AB is a chord parallel to pr such that $∠ B Q R = 70^{o}$ , then find $∠ A Q B$