the diameter of circle is 3cm AB and MN are two diameters perpendicular to each other In addition, CG - Maths - Circles

Question

the diameter of circle is 3cm AB and MN are two diameters
perpendicular to each other In addition, CG is perpendicular to ab
intersects AB at E such that AE:EB =1:2 and DF is perpendicular to
MN intersect MN at L and CG at H also NL:LM=1:2 then length of DH
is:
mam or sir please answer it is urgent

Manbar Singh · Accepted Answer

Dear Student,

Please find below the solution to the asked query :

<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/ck-files/ck_5625574bc5f15%20png"
style="width: 421px; height: 374px;">
We have,AB = MN = 3 cmNow, AEEB = NLLM = 12now, AB = 3cm ⇒AE + EB = 3⇒AE+2AE = 3 ⇒AE = 1cmSimilarly, we get NL = 1 cmNow, OA = AB2 = 1
5 cm and ON = MN2 = 1
5 cmNow, OE = OA - AE = 1
5 - 1 = 0
5 cmOL = ON - LN = 0
5 cmNow, quadrilateral EOLG is a square
So, HL = EO = 0 5 cmJoin OD
In ∆OLD,    OD2 = OL2 + DL2   Pythagoras theorem⇒DL2 = 1
52-0 52⇒DL2 = 2 25 - 0
25⇒DL2 = 2⇒DL = 2 cmNow, DH = DL - HL = 2 - 12 = 22 - 12 cm

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