Question

2. Prove that the perpendicular drawn from the centre to chord bisects the chord.
3. In the given figure, C and D are points on the semicircle and AB is the diameter.
ZBAD = 70° and 2DBC = 35°. Calculate ZABD and 2BDC.
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0
A​

Answer 1

Answer ⤵️

Given :

A chord PQ of a circle C(O,r) and perpendicular OL to the chord PQ.

To Prove :

LP=LQ

Construction :

Join OP and OQ.

Proof :

In triangles PLO and QLO,

OP=OQ=r

OL=OL

∠OLP=∠OLQ

So, by RHS-criterion of congruence,

△PLO≅△QLO

PL=LQ

Hence, proved.

Thus, the given statement is true.