In the given figure, three circles with centres A, B, C respectively t

1.	In the given figure, three circles with centres A, B, C respectively touch each other externally. If AB = 5 cm, BC = 7 cm and CA = 6 cm then the radius of the circle with centre A is(a) 1.5 cm (b) 2 cm (c) 2.5 cm (d) 3 cm
Answer» Correct answer is (b) 2 cm Given, AB = 5 cm, BC = 7 cm and CA = 6 cm. Let, AR = AP = x cm. BQ = BP = y cm CR = CQ = z cm (Since the length of tangents drawn from an external point arc equal) Then, AB = 5 cm \(\Rightarrow\) AP + PB = 5 cm \(\Rightarrow\) x + y = 5 ......(i) Similarly, y + z = 7 ....(ii) and z + x = 6 .........(iii) Adding (i), (ii) and (iii), we get: (x + y) + (y + z) + (z + x) = 18 \(\Rightarrow\) 2(x + y + z) = 18 \(\Rightarrow\) (x + y + z) = 9 ........(iv) Now, (iv) – (ii): \(\Rightarrow\) x = 2 ∴ The radius of the circle with center A is 2 cm.

In the given figure, three circles with centres A, B, C respectively touch each other externally. If AB = 5 cm, BC = 7 cm and CA = 6 cm then the radius of the circle with centre A is(a) 1.5 cm (b) 2 cm (c) 2.5 cm (d) 3 cm

Answer»

Correct answer is (b) 2 cm

Given, AB = 5 cm, BC = 7 cm and CA = 6 cm.

Let, AR = AP = x cm.

BQ = BP = y cm

CR = CQ = z cm

(Since the length of tangents drawn from an external point arc equal)

Then, AB = 5 cm

\(\Rightarrow\) AP + PB = 5 cm

\(\Rightarrow\) x + y = 5 ......(i)

Similarly, y + z = 7 ....(ii)

and z + x = 6 .........(iii)

Adding (i), (ii) and (iii), we get:

(x + y) + (y + z) + (z + x) = 18

\(\Rightarrow\) 2(x + y + z) = 18

\(\Rightarrow\) (x + y + z) = 9 ........(iv)

Now, (iv) – (ii):

\(\Rightarrow\) x = 2

∴ The radius of the circle with center A is 2 cm.

Discussion

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