You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Other

Quantitative Aptitude

Circles

In the given ...

Question

In the given figure, $A B$ is a diameter and $D C$ is tangent which meets AB extended to point C. If angle $∠ D A C = x^{o}$ , find in terms of $x^{o}$ :
i) $∠ D C B$
ii) $∠ D B C$

Open in App

Solution

$A B$ is diameter
$\Rightarrow ⌊ A D B = 90^{o}$
$⌊ D A C = x$ .
$\Rightarrow ⌊ A B D = 90 - x$
$\Rightarrow ⌊ D B C = 90 + x$
From alternative segment theorem
$⌊ B D C = ⌊ D A B$
$\Rightarrow ⌊ B D C = x$ .
$\Rightarrow ⌊ B C D = 90 - 2 x$
So, $i) ⌊ D C B = 90 - 2 x$
$i i) ⌊ D B C = 90 + x$

Suggest Corrections

Similar questions

In the given figure, AOB is a diameter and DC is parallel to AB. If $∠$ CAB = $x^{o}$ ; find (in terms of x) the values of :(i) $∠$ COB, (ii) DOC, (iii) $∠$ DAC,(iv) $∠$ ADC.

Q. Find

x^{o}, y^{o}, z^{o}

from the figure, where

A B = B D, B C = D C

and

∠ D A C = 30^{o}

In the given figure chord AB extended meets tangent DC at C. If AB = 7cm and BC =9 cm and area of $△ C B D = 18 c m^{2}$ ,

then find the area of $△ C A D .$

Q. In the given figure,

A B

is a diameter of a circle with centre

O

. If

A D E

and

C B E

are straight lines, meeting a

E

such that

∠ B A D = 35^{o}

and

∠ B E D = 25^{o}

, Then : (i)

∠ D C B

(ii)

∠ D B C

(iii)

∠ B D C

, are respectively.

In the given figure chord AB extended meets tangent DC at C. If AB = 7cm and BC =9 cm and area of $△ C B D = 18 c m^{2}$ ,

then area of $△ C A D =$ ______

Join BYJU'S Learning Program

In the given figure, AB is a diameter and DC is tangent which meets AB extended to point C. If angle ∠DAC=xo , find in terms of xo :i) ∠DCBii) ∠DBC

AB is diameter⇒⌊ADB=90o⌊DAC=x. ⇒⌊ABD=90−x⇒⌊DBC=90+xFrom alternative segment theorem ⌊BDC=⌊DAB ⇒⌊BDC=x.⇒⌊BCD=90−2xSo, i)⌊DCB=90−2xii)⌊DBC=90+x

In the given figure, $A B$ is a diameter and $D C$ is tangent which meets AB extended to point C. If angle $∠ D A C = x^{o}$ , find in terms of $x^{o}$ :
i) $∠ D C B$
ii) $∠ D B C$