Question

line l is the common tengent to both the circle tuching at point B and C line M is another tengent both are circle at point A then prove that angle BAC=90°,point D is the midpoint of seg BC. ​

Answer 1

We have

Then,

O and O

′

be the centre of two circles.

XY be a common tangent.

P is the mid point of OandO

′

.

Construct:-draw OX and OX

′

.

Then,

InΔOPXandO

′

PX

OP=O

′

P(radiusofcircle)

PX=PX(Commonline)

∠XPO=∠XPO

′

(Every90

o

)

Then,

ΔOPX≅ΔO

′

PX

So, OPO

′

are collinear

.

.

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