Question

11.In the given figure O is the centre and AE is the diameter
of the semicircle ABCDE. If AB = BC and ZAEC = 50°, the find angle CBE(b)angle CDE(C)angle AOB prove thatBOis parllel to CE​

Answer 1

In semi circle ABCDE, O is the centre, and AOE is the diameter, and AB= CD, Angle AEC= 50°,

we have to find out

a) CBE=?,

b) CDE=?

c) AOB=?

and prove BO parallel to CE,

we know that equal segment subtend equal angle at centre,

so angle COB =BOA

let BOA=x,

therefore:---

<COB = <BOA = x

as equal segment subtend equal angle at centre,

angleBEA = angleCEB= X/2 = 25° angle subtened at the centre is double angle  subtended at the circumferencr by same arc,

so angle AOB =50°

angle OCE = 50°  ( isosceles triangle),

by angle sum property angleCOE = 80°

angle CBE = 40°, angle subtend at centre is double angle subtended at circumferenc by same arc, angleCDE = 140° as BCDE is a quadrilateral ,angleBOC = angle OCE = 50°, by alternate interior property , we can say

BO|| CE.

Answer 2

Answer:

there is your answer good luck!