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Standard X

Mathematics

Tangent Perpendicular to Radius at Point of Contact

In the given ...

Question

In the given figure, PQ is a tangent to a circle with centre O. A is the point of contact. If $∠$ PAB = $67^{o}$ , then the measure of $∠$ AQB is

(a) $73^{o}$ (b) $64^{o}$ (c) $53^{o}$ (d) $44^{o}$

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Solution

<BAC=90
PAQ is a straight line
<PAB+ <BAC+ <CAQ=180°
67° + 90° + <CAQ = 180°
<CAQ=23°
<CBA = <CAQ( angle that subtend are same)
<BAQ+ <QBA+ <AQB=180°
(90°+23°)+23°+<AQB=180°
<AQB=44°

(d) 44° is correct option

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In the given figure, PQ is a tangent to a circle with centre O. A is the point of contact. If ∠ PAB = 67o, then the measure of ∠ AQB is (a) 73o (b) 64o (c) 53o (d) 44o

<BAC=90 PAQ is a straight line <PAB+ <BAC+ <CAQ=180° 67° + 90° + <CAQ = 180° <CAQ=23° <CBA = <CAQ( angle that subtend are same) <BAQ+ <QBA+ <AQB=180° (90°+23°)+23°+<AQB=180° <AQB=44° (d) 44° is correct option

In the given figure, PQ is a tangent to a circle with centre O. A is the point of contact. If $∠$ PAB = $67^{o}$ , then the measure of $∠$ AQB is

(a) $73^{o}$ (b) $64^{o}$ (c) $53^{o}$ (d) $44^{o}$

<BAC=90
PAQ is a straight line
<PAB+ <BAC+ <CAQ=180°
67° + 90° + <CAQ = 180°
<CAQ=23°
<CBA = <CAQ( angle that subtend are same)
<BAQ+ <QBA+ <AQB=180°
(90°+23°)+23°+<AQB=180°
<AQB=44°

(d) 44° is correct option