Question

in the given figure ap is the radius of circle abc and diameter of circle apq. prove that aq=qc se​

Answer 1

Step-by-step explanation:

Let AB be the chord of the given circle with centre O and a radius of 5 cm.

From O, draw OM perpendicular to AB.

Then OM = 3 cm and OB = 5 cm

From the right ΔOMB, we have:

OB2 = OM2 + MB2 (Pythagoras theorem)

⇒ 52 = 32 + MB2

⇒ 25 = 9 + MB2

⇒ MB2 = (25 − 9) = 16

⇒ MB=16 −−−√cm=4 cm

Since the perpendicular from the centre of a circle to a chord bisects the chord, we have:

AB = 2 × MB = (2 × 4) cm = 8 cm

Hence, the required length of the chord is 8 cm.