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Standard X

Mathematics

Two Circles Touching Internally and Externally

Three circles...

Question

Three circles with centres A, B and C touch each other as shown in the figure. If the radii of these circles are 8 cm, 3 cm and 2 cm respectively, find the perimeter of $△$ ABC.

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Solution

Let $r_{A} = 8 c m, r_{B} = 3 c m, r_{C} = 2 c m$

$A B = r_{A} - r_{B} = 8 - 3 = 5 c m$

$B C = r_{B} + r_{C} = 3 + 2 = 5 c m$

$C A = r_{A} - r_{C} = 8 - 2 = 6 c m$

$P = A B + B C + C A = 5 + 5 + 6 = 16 c m$

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Three circles with centres A, B and C touch each other as shown in the figure. If the radii of these circles are 8 cm, 3 cm and 2 cm respectively, find the perimeter of △ ABC.

Let rA=8cm,rB=3cm,rC=2cm AB=rA–rB=8–3=5cm BC=rB+rC=3+2=5cm CA=rA–rC=8–2=6cm P=AB+BC+CA=5+5+6=16cm

Three circles with centres A, B and C touch each other as shown in the figure. If the radii of these circles are 8 cm, 3 cm and 2 cm respectively, find the perimeter of $△$ ABC.

Let $r_{A} = 8 c m, r_{B} = 3 c m, r_{C} = 2 c m$

$A B = r_{A} - r_{B} = 8 - 3 = 5 c m$

$B C = r_{B} + r_{C} = 3 + 2 = 5 c m$

$C A = r_{A} - r_{C} = 8 - 2 = 6 c m$

$P = A B + B C + C A = 5 + 5 + 6 = 16 c m$