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Byju's Answer

Standard X

Mathematics

Length of Tangents Drawn from an External Point

In the adj. f...

Question

In the adj. figure, the circles with centres P and Q touch each other at R. A line passing through R meets the circles at A and B respectively.
Find $∠ R Q B$ if $∠ P A R = 35^{0}$

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Solution

$∵ A P = P R$
$∴ ∠ P A R = ∠ P R A = 35^{\circ}$
$(a n g l e s o p p o s i t e e q u a l s i d e s a r e e q u a l)$
$∴ ∠ Q R B = ∠ P R A = 35^{\circ}$
$(v e r t i c a l l y o p p o s i t e a n g l e s)$
$∠ Q R B = ∠ Q B R (a n g l e s o p p o s i t e e q u a l s i d e s a r e e q u a l)$
$∠ Q B R = ∠ Q R B = 35^{\circ}$
$I n △ Q R B => 35^{\circ} + 35^{\circ} + ∠ R Q B = 180^{\circ}$
$=> ∠ R Q B = 110^{\circ}$

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In the adj. figure, the circles with centres P and Q touch each other at R. A line passing through R meets the circles at A and B respectively.Find ∠RQB if ∠PAR=350

∵AP=PR∴∠PAR=∠PRA=35∘(anglesoppositeequalsidesareequal)∴∠QRB=∠PRA=35∘(verticallyoppositeangles)∠QRB=∠QBR(anglesoppositeequalsidesareequal)∠QBR=∠QRB=35∘In△QRB=>35∘+35∘+∠RQB=180∘=>∠RQB=110∘

In the adj. figure, the circles with centres P and Q touch each other at R. A line passing through R meets the circles at A and B respectively.
Find $∠ R Q B$ if $∠ P A R = 35^{0}$