Question

Example 2 If two intersecting chords of a circle make equal angles with the
passing through their point of intersection, prove that the chords are equal.
1474
You
Solution Given that AB and CD are two chords of
a circle, with centre O intersecting at a point E. PO
is a diameter through E, such that Z AEQ = 2 DEQ
(see Fig. 10.24). You have to prove that AB = CD.
Draw perpendiculars OL and OM on chords AB and
CD, respectively. Now
LOE = 180° - 90° - Z LEO = 90° - Z LEO
(Angle sum property of a triangle)
= 90° - Z AEQ = 90° - 2 DEQ
= 90° - ZMEO = Z MOE
E
Р
B
Fig. 1
In triangles OLE and OME,
Z LEO = ZMEO
Z LOE = Z MOE
(Provode
EO = EO
AOLF = A OME​

Answer 1

Answer:

ok just do it

Step-by-step explanation:

You

Solution Given that AB and CD are two chords of

a circle, with centre O intersecting at a point E. PO

is a diameter through E, such that Z AEQ = 2 DEQ

(see Fig. 10.24). You have to prove that AB = CD.

Draw perpendiculars OL and OM on chords AB and

CD, respectively. Now

LOE = 180° - 90° - Z LEO = 90° - Z LEO

(Angle sum property of a triangle)

= 90° - Z AEQ = 90° - 2 DEQ

= 90° - ZMEO = Z MOE

E

Р

B

Fig. 1

In triangles OLE and OME,

Z LEO = ZMEO

Z LOE = Z MOE

(Provode

EO = EO

AOLF = A OME