An arc of a circle subtends an angle of 70° at the centre. What is the measure of the angle subtended Class 9

An arc of a circle subtends an angle of 70° at the centre. What is the measure of the angle subtended Class 9

Question 1.

An arc of a circle subtends an angle of 70° at the centre. What is the measure of the angle subtended by the arc at a point on the circle? Class 9

Solution:

Angle subtended by arc at the centre(0) = 70° Since the angle subtended by an arc at the centre of the circle is double the angle subtended by the arc at any point on the circle.

∴ Angle subtended by the arc at a point on the circle = $\frac{\theta}{2}=\frac{70}{2}$ = 35°

Question 2.

The diameter of a circle is 26 cm. A chord of length 24 cm is drawn in the circle. Find the distance from the centre of the circle to the chord. Class 9

Solution:

Diameter of circle (d) = 26 cm

∴ Radius of circle = OA $=\frac{d}{2}$ = 13 cm

Chord length (AB) = 24 cm

Since the perpendicular from the centre of a circle to a chord bisects the chord.

∴ = $\frac{\mathrm{AB}}{2}=\frac{24}{2}$ = 12 cm

In right-angled ∆OMA

OA² = OM² + MA²

...[By Baudhayana-Pythagoras theorem]

∴ 13² = OM² + MA²

∴ 169 = OM² + 144

∴ OM² = 169 - 144

∴ OM² = 25

∴ OM = 5 cm

∴ The distance of the chord from the centre is 5 cm.