In the given figure, diameter of the semi-circle is 6 cm and CD=1 cm.
Find AB
√30
Given: AD=6 cm
CD=1 cm
⇒AC=AD−CD=6−1=5 cm
We have a property of chords which states that - If AB and CD are two chords of a circle intersecting at O, then AO x OB = CO x OD
Hence, we have BC2=AC×CD (We have BC2 as the perpendicular from the centre bisects the chord)
BC2=5×1
BC=√5
In △ACB, applying Pythagoras Theorem, we get,
AB2=AC2+BC2
⇒AB2=52+√52
=25+5=30
⇒AB=√30 cm