Question

4. Draw a circle with centre 0 and diameter AB = 26 cm. AC and BC are two chords of the circle, BC = 10 cm, OD is a perpendicular to the chord BC and OD = 8 cm. Verify whether the following statements are true or not:
a. AC = 20D. b. angleBOD = angleBAC​

Answer 1

Answer:

Perpendicular from the centre of a circle to a chord bisects the chord 

We know that OB⊥AB

From the figure we know that D is the midpoint of AB

We get 

AD=BD

We also know that O is the midpoint of BC

We get

OC=OB

Consider △ABC

Using the midpoint theorem

We get OB∥AC and 

OD=1/2 × AC

By cross multiplication 

AC=2×OD

Therefore, it is proved that AC∥DO and AC=2×OD