Question

CLOGUILLET MILL- GADU Point P is on the circle. If AB is diameter of the circle, then ZABP is K(A) a reflex angle (B) an acute angle (C) a right angle (D) an obtuse angle

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Answer 1

Step-by-step explanation:

Since BK⊥HM,AH⊥HM and OP⊥HM. Therefore,

AH∥OP∥BK

Let AH=x,BK=y and OP=r. Further, let BM=z.

In △MKB and △MHA, we have

∠MKB=∠MHA=90

o

and ∠BMK=∠AMH

So, by AA criterion of similarity, we have

△MKB∼△MHA

⇒

AH

BK

=

MA

MB

⇒

x

y

=

2r+z

z

⇒2ry+yz=zx⇒z=

x−y

2ry

. . . (i)

In △MKB and △MPO, we have

∠MKB=∠MPO=90

o

∠BMK=∠OMP

So, by AA criterion of similarly, we have

△MKB∼△MPO

⇒

OP

BK

=

OM

BM

⇒

r

y

=

r+z

z

⇒ry+yz=rz

⇒z=

r−y

ry

. . . (ii)

From(i) and (ii), we get

r−y

ry

=

x−y

2ry

⇒2r−2y=x−y

⇒2r=x+y

⇒AB=AH+BK