Question

In given figure, o is the center of the circle. Find value of x

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Answer 1

$\huge{ \star{ \mathfrak{ \underline{✤Soution}}}}$

$\sf{In \: the \: given \: figure, }$

$\sf{ \angle{CAD = x \: and{ \angle{BAD = 2x}}}}$

$\sf{According \: to \: the \: circle \: concept}$

$\sf{ \angle{CAD = { \angle{CBD}}}}$

$\sf{so \: { \angle{CBD= x}}}$

$\sf{also \: line \: BC \: contains \: central \: of \: circle}$

$\sf{hence { \triangle{CBD \: is \: right \: angle \: triangle}}}$

$\sf{hence { \angle{CDB= 90{ \degree}}}}$

$\sf{ \blue{We \: know \: that \: sum \: of \: all \: angles \: of \: a \: triangle \: is \: 180{ \degree}}}$

$\sf{Hence,{ \angle{BCD + { \angle{CBD + { \angle{CDB= 180{ \degree}}}}}}}}$

$\sf{ = > 2x + x + 90 = 180{ \degree}}$

$\sf {= > 3x = 180{ \degree{ - 90{ \degree}}}}$

$\sf{ = > x = \frac{90}{3} { \degree}}$

$\sf{ \green{hence \: x = 30{ \degree}}}$

Hope this helps you mate ✌