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Question

In ΔABC,AB=BC=6cm. A circle is drawn with center at B and radius 2 cm. What is the scale factor of the triangle formed by the point B and the points where the circle intersects ABC?

A
23
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B
1
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C
13
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D
12
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Solution

The correct option is C 13

Given in ΔABC,AB=BC=6cm.
If a circle is drawn with B as center and 2 cm radius,
it intersects ΔABC at 2 points D and E.
BD=BE=2cm.
In ΔABC and ΔEBD,
BEAB=BDBC=26=13 and EBD=ABC.
By SAS similarity, ΔABC and ΔEBD
are similar.
The scale factor for the ΔEBD
with respect to ΔABC is 13.

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