Chords and their Distances from the Centre | Circles | Assessment | English | Grade 9

The longest chord of the circle is _____

• AB

• RS

• PQ

• CD

Answer explanation

The longest chord of the circle is PQ.

Segment of a circle is the region between an arc and _____of the circle.

• Diameter

• Chord

• Radius

• Centre

Answer explanation

Segment of a circle is the region between an arc and chord of the circle.

An arc is a ________ when its ends are the ends of a diameter.

• Minor segment

• Chord

• Major Segment

• Semi - circle

Answer explanation

An arc is a semi - circle when its ends are the ends of a diameter.

Tags

CCSS.HSG.C.A.2

The radius of the circle is 5 cm and distance of the chord from the centre of the circle is 4 cm. Then the length of the chord is ______

• 3 cm

• 9 cm

• 6 cm

• 12 cm

Answer explanation

In △ ODA, (By using Pythagoras theorem) OA² = OD² + AD² 5² = 4² + (AD)² AD² = 25 - 16 AD² = 9 AD = 3 cm We know that perpendicular drawn from centre bisects the chord therefore, Chord AB = 2(AD) = 2 x 3 = 6 cm

Tags

CCSS.HSG.C.A.2

A circle of centre O has radius ON equals to 10cm. The length of a chord MN of the circle is 12 cm. Then the distance of the chord from the center is _____.

• 8 cm

• 16 cm

• 10 cm

• 14 cm

Answer explanation

We know that perpendicular drawn from centre bisects the chord therefore, PM = PN = 1/2MN = 1/2 × 12 = 6 cm Radius OM = 10 cm In right △OXP OM² = MP² + OP² (10)² = (6)² + OP² OP² = (10)² - (6)² OP² = 100 - 36 OP² = 64 OP = √64 OP = 8 cm

Tags

CCSS.HSG.C.A.2

The length of a chord of a circle is 4 cm. If its distance from the centre is 1.5 cm. Then the radius of the circle is ___.

• 3 cm

• 5 cm

• 2.5 cm

• 4.5 cm

Answer explanation

The perpendicular drawn from centre bisects the chord therefore, AP = PB = 1/2 AB = 1/2 x 4 = 2 cm In right △OPA OA² = OP² + PA² OA² = (1.5)² + (2)² OA² = 2.25 + 4 OA² = 6.25 OA = √6.25 OA = 2.5 cm

Tags

CCSS.HSG.C.A.2

Two points P and Q are 16 cm apart. A circle with radius 17 cm is drawn to pass through these points. Find the distance of PQ from the centre of the circle.

• 15 cm

• 18 cm

• 14.5 cm

• 12.5 cm

Answer explanation

We know that perpendicular drawn from centre bisects the chord therefore, PD = DQ = 1/2PQ = 1/2 × 16 = 8 cm Radius OP = 17 cm In right △ODP OP² = OD² + PD² (17)² = OD² + (8)² OD² = (17)² - (8)² OD² = 289 - 64 OD² = 225 OD = √225 OD = 15 cm

Tags

CCSS.HSG.C.A.2