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In the figure PQR is a …

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In the 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= ?

Posted by Fehmina Tabassum 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

Given,

AB II PR
{tex}\angle{/tex}B = {tex}\angle{/tex}Q [Alternate interior angles]
{tex}\angle{/tex}B = 70^o
{tex}\triangle{/tex}AQB is an Isosceles triangle,
AQ = BQ
So, {tex}\angle{/tex}BQR = {tex}\angle{/tex}BAQ
{tex}\angle{/tex}A = 70^o
In {tex}\triangle{/tex}AQB,
{tex}\angle{/tex}QAB+ {tex}\angle{/tex}ABQ + {tex}\angle{/tex}BQA = 180^o
{tex}\Rightarrow{/tex} {tex}70° + 70° +{/tex} {tex}\angle{/tex}{tex}Q = 180^o{/tex}
{tex}\Rightarrow{/tex} {tex}\angle{/tex}B{tex}QA = 180^o - 140^o = 40^o{/tex}

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