AD is the diameter of a circle and AB is the chord if AD=34cm,AB=30cm,then find the distance of the - Maths - Circles

Question

AD is the diameter of a circle and AB is the chord if
AD=34cm,AB=30cm,then find the distance of the chord AB from the
centre of the circle reply fast

Vimala · Accepted Answer

Let us observe the following diagram:

AD is the diameter of the circle whose length is AD = 34 cm AB is the chord of the circle whose length is AB = 30 cm Distance of the chord from the centre is OM Since the line through the centre to the chord of the circle is the perpendicular bisector, we have $∠ O M A = 90^{\circ}$ and AM = BM Thus, $Δ A M O$ is a right triangle Apply Pythagorean Theorem: Thus, $O A^{2} = A M^{2} + O M^{2} (1)$ Since the diameter AD = 34 cm , radius of the circle is 17 cm Thus, OA = 17 cm Since AM = BM and AB = 30 cm, we have AM = BM = 15 cm Substitute the values of OA and AM in equation (1), we have $O A^{2} = A M^{2} + O M^{2} 17^{2} = 15^{2} + O M^{2} 289 = 225 + O M^{2} O M^{2} = 64 O M = 8$ Thus, the perpendicular distance from the centre to the chord AB of the circle is 8 cm

AD is the diameter of a circle and AB is the chord. if AD=34cm,AB=30cm,then find the distance of the chord AB from the centre of the circle.....reply fast