Question

- O is the centre of the circle having radius 5 cm. AB and AC are two chords such that AB = AC 6 cm. If OA meets BC at M, then OM (1) 3.6 cm (2)1.4 (3) 2 cm (4) 3 cm ​

Answer 1

option b) 1.4 is correct answer

M is the mid point of BC

Thus, BM=MC=x [Let]

OA is the radius of the circle

Let AM=y

OM=OA−AM

OM=5−y ----(i)

Now, △ABM is a right angled triangle

∴AB 2 =AM 2 +BM 2

=>6 power2=y 2+x 2

=>x 2 =36−y 2 -----(ii)

Again in △OMB

OB 2 =OM2 +BM 2

=>52=(5−y) 2 +x 2

....[Using (i)]

=>25=25−10y+y

2

+36−y

2

....[Using (ii)]

=>10y=36

=>y=3.6

Thus, OM=(5−3.6)=1.4cm