Q. 64.0( 25 Votes )

# In the figure 6.21, CD is a diameter of the circle with center O. Diameter CD is perpendicular to chord AB at point E. Show that ΔABC is an isosceles triangle.

We know that a perpendicular drawn from the center of a circle on its chord bisects

the chord.

So, AE = EB

In ΔACE and ΔBCE,

AE = EB

AEC = BEC = 90°

CE = CE (common)

Δ ACE Δ BCE (By SAS congruence)

Therefore, AC = BC (by CPCT)

Hence proved that ABC is an isosceles triangle.

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