### Video Transcript

π΄, π΅, πΆ, and π· are points on
the circumference of a circle. π΄ππΆ and π·ππ΅ are straight
lines. The following lengths are given:
π΄π· is equal to 57 over four, ππ· is equal to 12, and πΆπ is equal to four. Based on this information, find the
length of π΅πΆ.

Using our angle properties, we can
see that angle π΄ππ· is equal to angle π΅ππΆ as they are opposite angles. The angles π·π΄π and ππ΅πΆ are
also equal as they have a shared arc β the arc π·πΆ. This means that they are angles in
the same segment and theyβre therefore equal. The angles π΄π·π and ππΆπ΅ are
equal for the same reason. This time their shared arc is the
arc π΄π΅. We can therefore say that triangle
π΄ππ· and triangle π΅ππΆ are similar as all three angles are equal.

In order to work out the length
π΅πΆ, we firstly need to find the scale factor. As triangle π΅ππΆ is smaller than
triangle π΄ππ·, the scale factor will be a reduction. The scale factor is equal to four
twelfths. This can be simplified to
one-third. Therefore, triangle π΅ππΆ is a
third of the size of triangle π΄ππ·. In order to calculate the length of
π΅πΆ or π₯, we need to multiply 57 divided by four β fifty-seven quarters β by
one-third. Simplifying this calculation gives
us 19 quarters multiplied by one. 19 multiplied by one is 19 and four
multiplied by one is equal to four.

This means that the length of π΅πΆ
is 19 over four or nineteen quarters. This could be rewritten as a
decimal as 4.75.