91Ó°ÊÓ

Two tangents circles; $EF$is a common external tangent;

$GH$is the common internal tangent.

For the larger circle, $EG$and $GH$ are two tangents drawn from a common point $G$.

By the property of tangents,

if two tangents of the circle are drawn from a common point, then their length are equal.

Thus, $EG=GH$ …(¾±)

Now, for the smaller circle, $GH$ and $FG$ are two tangents drawn from a common point $G$.

By the property of tangents,

if two tangents of the circle are drawn from a common point, then their length are equal.

Thus, $FG=GH$…(¾±¾±)

We get,

$EG=FG$

Hence, G is the midpoint of the common external tangent $EF$of both the circle.

Therefore, $G$is the midpoint of external tangent $EF$.

Two tangents circles; $EF$ is a common external tangent;

$GH$ is the common internal tangent.

Since, $EG=GH=GF$

A circle can be constructed with G as the center and $EG=GH=GF$as radius.

In the circle with center G, $EF$ is the diameter and angle $∠EHF$ is made in the semicircular arc $EHF$.

Any angle made in a semicircular arc is always a right angle, it can be easily said that $∠EHF$is a right angle.

So, $\mathrm{Δ}EHF$ is a right angled triangle and $∠EHF={90}^0.$

Therefore, Value of, $m∠EHF={90}^0$.