Question

Two equal chords AB and DC 10 cm each, are produced to meet at E. If DE = 5 CM (i) find AE (ii) If OL = 5 cm find OE, where L is the mid point  of AB.     ​

Answer 1

ANSWER

O is the centre.

Given:-OM⊥AB.....(1)

ON⊥CD......(2)

and AB⊥CD.....(3)

⇒AB∣∣ONandCD∣∣DM

from (2) and (3) from (1) and (3)

⇒

MP∣∣ONandPN∣∣OM

(4) (5)

∴OMPN is a parallelogram.

(since opposite side are parallel.)

But angle ∠ONP=90

0

=(Given)

∠NPM=90

0

(Given)

∠NPM=∠NOM [opposite angles of parallelogram]

∴ all angles in the parallelogram are 90

0

∴OMPN is a square or rectangle.

∴ length of perpendicular from centre to equal chords are equal.

⇒ON=OM

adjacent sides of rectangular OMPN are equal.

⇒

OMPNisasquare

Answer 2

Answer:

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