Question

please answer this
I will mark the best answer as brainliest ​

Answer 1

Answer:

a = 12 , b = 8 , c = 7

Step-by-step explanation:

From the figure we get to know that the external points of the circle of circle A, B, & C are the tangents and

AB = 20 CM , BC = 15 CM , AC = 19 CM

We know that the tangents drawn from the external points of the circle are equal.

AR = AQ = a

BR = BP = b

CP = CQ = c

Given AB = 20 CM , BC = 15 CM , AC = 19 CM

AB = AR + BR

a + b = 20 ----------(1)

BC = BP + CP

b + c = 15 ----------(2)

AC = AQ + CQ

a + c = 19 ---------(3)

By adding equation (1), (2) and (3), we get-

(a + b) + (b + c) + (a +c) = 20 + 15 + 19

2a + 2b + 2c = 54

(a + b + c) = 27 ----------(4)

Now, we will substitute equation (1) in equation (4). So, we get –

(a + b) + c = 27

20 + c = 27

$\boxed{c = 27 - 20 = 7}$

Now, we will substitute the value of ‘c’ in equation (3)

a + c = 19

a + 7 = 19

$\boxed{a = 19 - 7 = 12}$

By substituting the value of ‘c’ in equation (2), we get

b + c = 15

b + 7 = 15

$\boxed{b = 15 - 7 = 8}$

Therefore,

AR = AQ = a =  12

BR = BP = b = 8

CP = CQ = c = 7