Question

In the figure M is the centre of the circle. AB and CD are parallel chords. The diameter of the circle is 30 cm, AB = 18cm and CD = 24 cm
1.) find the distance from the centre to AB.
2.) Find the distance between AB and CD.

*no unwanted answer needed. ​

Answer 1

Step-by-step explanation:

here we use simple geometry Hope u get ur answer

Answer 2

Answer:

12, 21

Step-by-step explanation:

Diameter = 30 cm => Radius = 15 cm.

Join MA, MB, MC, MD.

Draw a perpendiculars MX and MY intersecting AB at X and CD at Y respectively. Since MAB and MCD are isosceles triangles by definition, MX and MY are perpendicular bisectors (can easily prove this by congruency, but is trivial so proof not needed).

Using Pythagoras Theorem, we get

MX^2 + AX^2 = AM^2

AM is radius and MX is half of AB

=> MX^2 = 15^2 - 9^2 = 225 - 81 = 12^2 => MX = 12

(MX = Distance from center to AB)

Similarly for triangle MCD, we get

MY^2 = MC^2 - CY^2 = 15^2 - 12^2 = 9^2 => MY = 9. (MY = Distance from center to CD).

Distance between AB and CD = 12 + 9 = 21.