AB is a diameter of a circle. M is a point in AB such that AM = 18 cm and MB = 8 cm. Find the length of the shortest chord through M.

Given, AM = 18 cm and MB = 8 cm From figure, AB = AM + MB = 18 + 8 = 26 cm Radius of the circle = = 13 cm. Let CD is the shortest chord drawn through M. ∴ CD ⊥ AB From figure, OM = AM - AO = 18 - 13 = 5 cm OC (radius) = OA = 13 cm Now in right ∆OMC, OC 2 = OM 2 + MC 2 (By pythagoras theorem) 13 2 = 5 2 + MC 2 MC 2 = 13 2 - 5 2 MC 2 = 169 - 25 = 144 MC = = 12 cm. M is Mid-Point of CD (As perpendicular from center to the chord bisects it.) CD = 2 × MC = 2 × 12 = 24 cm. Hence, length of shortest chord = 24 cm.

View Answer Bookmark Now

An equilateral triangle of side 6 cm is inscribed in a circle. Find the radius of the circle.

View Answer Bookmark Now

A rectangle with one side of length 4 cm is inscribed in a circle of diameter 5 cm. Find the area of rectangle.

View Answer Bookmark Now

The length of the common chord of two intersecting circles is 30 cm. If the radii of the two circles are 25 cm and 17 cm, find the distance between their centres.

View Answer Bookmark Now

Mathematics

AB is a diameter of a circle. M is a point in AB such that AM = 18 cm and MB = 8 cm. Find the length of the shortest chord through M.

Circles

Related Questions

An equilateral triangle of side 6 cm is inscribed in a circle. Find the radius of the circle.

A rectangle with one side of length 4 cm is inscribed in a circle of diameter 5 cm. Find the area of rectangle.

The length of the common chord of two intersecting circles is 30 cm. If the radii of the two circles are 25 cm and 17 cm, find the distance between their centres.