Question

The radii of two circles are 25 cm and 9 cm . The distance between their centres is 34 cm. State the true statement of the following:

i. The circles touch in two distinct points.
ii. The circles touch internally.
iii. The circles touch externally
iv. The circle do not touch.​

Answer 1

length of the common tangents is 30 cm

The radii of two circles are r₁ = 25 cm and r₂ = 9 cm.

distance between their center = r₁ + r₂ = 25 + 9 = 34 cm [ externally touch each other ]

length of common tangents of these circles = √{(distance between centres)² - (r₁ - r₂)²}

= √{(34)² - (25 - 9)²}

= √{(34 - 16)(34 + 16)}

= √{18 × 50}

= √{900}

= 30 cm

hope it helps dear..........