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Relations Using Incircle and Outcircle

Draw triangle...

Question

Draw triangle ABC, in which BC = 8 cm, AC = 7 cm and AB = 6 cm with A, B and C as centre. Draw circles of radii 2.5 cm, 3.5 cm and 4.5 cm respectively and show that these circles touch in pairs

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Solution

The sides of triangle ABC are AB = 6 cm, BC = 8 cm and AC = 7 cm.

The radii of the circles with centers A, B and C are r₁ = 2.5 cm, r₂ = 3.5 cm and r₃ = 4.5 cm respectively.

(i) It is given that AB = 6 cm

Here, r₁ + r₂ = 2.5 + 3.5 = 6 cm

We observe that the distance between the centers of the circles and the sum of their radii are equal.

Hence, the circles touch each other externally.

(ii) It is given that BC = 8 cm

Here, r₂ + r₃ = 3.5 + 4.5 = 8 cm

We observe that the distance between the centers of the circles and the sum of their radii are equal.

Hence, the circles touch each other externally.

(iii) It is given that, AC = 7 cm

Here, r₁ + r₃ = 2.5 + 4.5 = 7 cm

We observe that the distance between the centers of the circles and the sum of their radii are equal.

Hence, the circles touch each other externally.

Thus, the three circles touch each other in pairs.

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