Multiple choice

MN is tangent to a circle, with center O and radius 6cm, at point X. If ON = 10 cm and OM = 37/2 cm, then find the length of MN?

  1. 35 cm

  2. 25.5 cm

  3. 27.5 cm

  4. 55 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Since MN is tangent at X, OX is perpendicular to MN. Using right triangles: In triangle OXN, ON² = OX² + XN², so 100 = 36 + XN², giving XN = 8 cm. In triangle OXM, OM² = OX² + XM², so (37/2)² = 36 + XM² = 1369/4, giving XM² = 1369/4 - 144/4 = 1225/4, so XM = 35/2 = 17.5 cm. Therefore, MN = XM + XN = 17.5 + 8 = 25.5 cm.

Keep practicing — related questions