Question

AB = 6cm BC = 10cm CA=14cm. Find value o f x and y and z?​

Answer 1

Answer:

• Value of x is 1 cm, y is 9 cm and z is 5 cm.

Step-by-step explanation:

In given figure AB, BC and AC are tangents of circle which are having measure 6 cm, 10 cm and 14 cm respectively.

Tangent AB is touching the circle at point P.

Similarly,

BC at point R

And, AC at point Q.

We know,

The lengths of tangents drawn from an external point to a circle are equal.

So, BP = x, RC = y and AQ = z

⇒x = BP

⇒x = AB - z

⇒x = 6 - z --------(i)

⇒y = RC

⇒y = BC - x

⇒y = 10 - x --------(ii)

⇒z = AQ

⇒z = AC - y

⇒z = 14 - y ---------(iii)

Now, Take any one equation:

⇒x = 6 - z

• Put z = 14 - y

⇒x = 6 - 14 - y

• Put y = 10 - x

⇒x = 6 - 14 - 10 - x

⇒x + x = 6 - 4

⇒2x = 2

⇒x = 2/2

⇒x = 1

Put value of x in equation (ii) :

⇒y = 10 - x

⇒y = 10 - 1

⇒y = 9

Put value of y in equation (iii) :

⇒z = 14 - y

⇒z = 14 - 9

⇒z = 5

Therefore,

Value of x is 1 cm, y is 9 cm and z is 5 cm.

Answer 2

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Let BD = x

Then DC = 12-x

Ratio of AB/AC=BD/DCAB/AC=BD/DC

SO , 10/6=x/(12−x)10/6=x/(12−x)

120−10x=6x120−10x=6x

16x = 120

x = 120/16 = 15/2=7.5cm15/2=7.5cm

BD = 15/215/2

DC = 12−15/2=9/2=4.5cm12−15/2=9/2=4.5cm