Same chapter3 marksDifficulty: Medium
A tangent to a circle of radius 8 cm is drawn from a point 17 cm from the centre. Find the length of the tangent.
Circles
3 marksDifficulty: Medium
Draw a circle with centre O and a chord AB. Mark a point C on the major arc and a point D on the minor arc. Show on your diagram why angle ACB and angle ADB are supplementary.
Original Khojo Papers practice question — not from a past board paper.
Answer
ACBD is a cyclic quadrilateral, so its opposite angles ACB and ADB add up to 180°.
No citable source has been recorded for this record. Treat it as practice material, not as fact.
Explanation
C and D lie on opposite arcs, so ACBD is a cyclic quadrilateral and the opposite angle property applies.
Related questions
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Same chapter3 marksDifficulty: Medium
In a circle of radius 13 cm, a chord is at a distance of 5 cm from the centre. Find the length of the chord.
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Same chapter3 marksDifficulty: Medium
From an external point P two tangents PA and PB are drawn to a circle with centre O. If angle APB = 60°, find angle AOB.
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Same chapter3 marksDifficulty: Medium
Two chords AB and CD of a circle intersect inside the circle at P. If PA = 4 cm, PB = 6 cm and PC = 3 cm, find PD.
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PT is a tangent from an external point P to a circle, and PAB is a secant through P meeting the circle at A and B. If PT = 6 cm and PA = 4 cm, find PB.
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Same chapter2 marksDifficulty: Medium
Assertion: a parallelogram inscribed in a circle must be a rectangle. Reason: the opposite angles of a cyclic quadrilateral are supplementary. State whether both are true and whether the reason explains the assertion.
Circles