Q. 465.0( 1 Vote )

# The question cons

Answer : Assertion (A):

Construction: Draw a Δ ABC in which AB = AC, Let O be the midpoint of AB and with O as centre and OA as radius draw a circle, meeting BC at D

Now, In Δ ABD

ADB = 90° (angle in semicircle)

Also, ADB + ADC = 180°

90° + ADC = 180°

ADC = 180° – 90°

ADC = 90°

Consider Δ ADB and Δ ADC

Here,

AB = AC (given)

AD = AD (common)

ADB = ADC ( 90° )

By SAS congruency, Δ ADB Δ ADC

So, BD = DC(C.P.C.T)

Thus, the given circle bisects the base. So, Assertion (A) is true

Reason (R) :

Let BAC be an angle in a semicircle with centre O and diameter BOC

Now, the angle subtended by arc BOC at the centre is BOC = 2× 90°

BOC = 2× BAC = 2× 90°

So, BAC = 90° (right angle)

So, reason (R) is true

Clearly, reason (R) gives assertion (A)

Hence, correct choice is A

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