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Standard X

Mathematics

Intersection between Tangent and Secant

In the given ...

Question

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 $△ C A D =$ ______

$16 c m^{2}$

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$24 c m^{2}$

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$32 c m^{2}$

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$64 c m^{2}$

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Solution

The correct option is C
$32 c m^{2}$

CD is a tangent to the circle (given)

$C D^{2} = C B \times C A$

$C D^{2} = 9 \times 16$

CD = 12cm

Hence, $∠ B D C = ∠ D A B$ (angles in the alternate segment are equal)

$△ C D B \approx △ C A D$ (AA similarity)

$△ C D B / △ C A D = \frac{B C^{2}}{C D^{2}}$

$\frac{18}{△ C A D} = {(\frac{9}{12})}^{2}$

$\frac{18}{△ C A D} = {(\frac{3}{4})}^{2}$

$\frac{18}{△ C A D} = (\frac{9}{16})$

$△ C A D = 32 c m^{2}$

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Similar questions

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 $△ C A D =$ ______

Q. Triangles ABC and DEF are similar.

(i) If area (∆ABC) = 16 cm², area (∆DEF) = 25 cm² and BC = 2.3 cm, find EF.
(ii) If area (∆ABC) = 9 cm², area (∆DEF) = 64 cm² and DE = 5.1 cm , find AB.
(iii) If AC = 19 cm and DF = 8 cm, find the ratio of the area of two triangles.
(iv) If area (∆ABC) = 36 cm², area (∆DEF) = 64 cm² and DE = 6.2 cm, find AB.
(v) If AB = 1.2 cm and DE = 1.4 cm, find the ratio of the areas of ∆ABC and ∆DEF.

Q. Triangles ABC and DEF are similar.

(i) If area (

△ A B C

)= 16

{cm}^{2}

, area(

△

DEF)= 25

{cm}^{2}

and

B C = 2.3 cm

, find

E F

(ii) If area (

△ A B C

)= 9

{cm}^{2}

, area(

△

DEF) = 64

{cm}^{2}

and

D E = 5.1 cm

, find

A B

(iii) If

A C = 19 cm

and

D F = 8 cm

, find ratio of the area of two triangles.

(iv) If area (

△ A B C

)= 36

{cm}^{2}

, area (

△

DEF) =64

{cm}^{2}

and

D E = 6.2 cm

, find

A B

(v) If

A B = 1.2 cm

and

D E = 1.4 cm

, find the ratio of the areas of triangle

A B C

and

D E F

Question 16

The figure ABCD is a quadrilateral in which AB = CD and BC = AD. Its area is

(a) $72 c m^{2}$ (b) $36 c m^{2}$ (c) $24 c m^{2}$ (d) $18 c m^{2}$

If the length of any face diagonal of a cube is 4√2 cm, then the difference between its total surface area and its lateral surface area is:
A) 16 cm $^{2}$ B) 24 cm $^{2}$
C) 64 cm $^{2}$ D) 32 cm $^{2}$

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In the given figure chord AB extended meets tangent DC at C. If AB = 7cm and BC =9 cm and area of △CBD=18cm2, then area of △CAD= ______

The correct option is C 32 cm2 CD is a tangent to the circle (given) CD2=CB×CA CD2=9×16 CD = 12cm Hence, ∠BDC=∠DAB (angles in the alternate segment are equal) △CDB≈△CAD (AA similarity) △CDB/△CAD=BC2CD2 18△CAD=(912)2 18△CAD=(34)2 18△CAD=(916) △CAD=32cm2

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 $△ C A D =$ ______