Question

an isosceles traingle is inscribed in a circle with PQ =PR=25cm andQR =14cm.Find the radius of the circle.

Answer 1

QR=14cm that is diameter of circle.
So QR/2=radius
=14/2=7cm
Hope it will help u ...

Answer 2

Make the triangle PQR inside a circle.

PQ=25,QR=25 and PR=14

Draw a perpendicular from Q to the base PR which divides PR in two equal parts.

Let that dividing point be S.

Now draw a perpendicular from point P to the line QS dividing it into two equal halves.Let that point be T.

Now you know what PT is,it is the radius of the circle.

To find it just use pythagoras theorem in triangle PQS:

QS²=PQ²-PS² (PS=PR/2=7, PQ=25(Given))

QS=24 (After Solving)

Now we have ST=QS/2=12 and PS=7

In triangle PST,using Pythagoras theorem:

PT²=PS²+ST²=193

so radius=PT=√193